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Comput. 218(9), 5806–5818 (2012)",{"doi":274},{"id":445,"text":446,"url":447,"identifiers":448},"2c779217-ec3e-4604-9cd5-b712a25999d3","Liu, C., Wu, X.: The boundness of the operator-valued functions for multidimensional nonlinear wave equations with applications. Appl. Math. Lett. 74, 60–67 (2017)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0893965917301398",{"doi":449},"10.1016\u002Fj.aml.2017.04.026",{"id":270,"text":451,"url":272,"identifiers":452},"Lin, X., Zhao, Z.: Iterative technique for third-order differential equation with three-point nonlinear boundary value conditions. Electron. J. Qual. Theory Differ. Equ. 2016, 12 (2016)",{"doi":274},{"id":270,"text":454,"url":272,"identifiers":455},"Pan, Y., Yu, H.: Biomimetic hybrid feedback feedforward neural-network learning control. IEEE Trans. Neural Netw. Learn. Syst. 28(6), 1481–1487 (2017)",{"doi":274},{"id":270,"text":457,"url":272,"identifiers":458},"Liu, H., Li, S., Wang, H., Huo, Y., Luo, J.: Adaptive synchronization for a class of uncertain fractional-order neural networks. Entropy 17(10), 7185–7200 (2015)",{"doi":274},{"id":270,"text":460,"url":272,"identifiers":461},"Liu, H., Li, S., Wang, H., Sun, Y.: Adaptive fuzzy control for a class of unknown fractional-order neural networks subject to input nonlinearities and dead-zones. Inf. Sci. 454–455, 30–45 (2018)",{"doi":274},{"id":270,"text":463,"url":272,"identifiers":464},"Dong, W., Farrell, J.A., Polycarpou, M.M., Djapic, V., Sharma, M.: Command filtered adaptive backstepping. IEEE Trans. Control Syst. Technol. 20(3), 566–580 (2012)",{"doi":274},{"id":270,"text":466,"url":272,"identifiers":467},"Pan, Y., Yu, H.: Composite learning from adaptive dynamic surface control. IEEE Trans. Autom. Control 61(9), 2603–2609 (2016)",{"doi":274},{"id":270,"text":469,"url":272,"identifiers":470},"Li, F., Gao, Q.: Blow-up of solution for a nonlinear Petrovsky type equation with memory. Appl. Math. Comput. 274, 383–392 (2016)",{"doi":274},{"id":472,"text":473,"url":474,"identifiers":475},"6edfe3dd-859e-46b4-9f53-d79aacd08d2f","Gao, L., Wang, D., Wang, G.: Further results on exponential stability for impulsive switched nonlinear time-delay systems with delayed impulse effects. Appl. Math. Comput. 268, 186–200 (2015)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0096300315008048",{"doi":476},"10.1016\u002Fj.amc.2015.06.023",{"id":270,"text":478,"url":272,"identifiers":479},"He, X., Qian, A., Zou, W.: Existence and concentration of positive solutions for quasilinear Schrödinger equations with critical growth. Nonlinearity 26(12), 3137 (2013)",{"doi":274},{"id":270,"text":481,"url":272,"identifiers":482},"Feng, Y.-H., Liu, C.-M.: Stability of steady-state solutions to Navier–Stokes–Poisson systems. J. Math. Anal. Appl. 462(2), 1679–1694 (2018)",{"doi":274},{"id":18,"text":484,"url":18,"identifiers":485},"Bai, Y., Mu, X.: Global asymptotic stability of a generalized sirs epidemic model with transfer from infectious to susceptible. J. Appl. Anal. Comput. 8(2), 402–412 (2018)",{},{"id":270,"text":487,"url":272,"identifiers":488},"Cao, X., Wang, J.: Finite-time stability of a class of oscillating systems with two delays. Math. Methods Appl. Sci. 41(13), 4943–4954 (2018)",{"doi":274},{"id":270,"text":490,"url":272,"identifiers":491},"Shen, T., Xin, J., Huang, J.: Time–space fractional stochastic Ginzburg–Landau equation driven by Gaussian white noise. Stoch. Anal. Appl. 36(1), 103–113 (2018)",{"doi":274},{"id":270,"text":493,"url":272,"identifiers":494},"Li, M., Wang, J.: Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations. Appl. Math. Comput. 324, 254–265 (2018)",{"doi":274},{"id":270,"text":496,"url":272,"identifiers":497},"Liu, S., Wang, J., Zhou, Y., Fečkan, M.: Iterative learning control with pulse compensation for fractional differential systems. Math. Slovaca 68(3), 563–574 (2018)",{"doi":274},{"id":270,"text":499,"url":272,"identifiers":500},"Zhang, J., Wang, J.: Numerical analysis for Navier–Stokes equations with time fractional derivatives. Appl. Math. Comput. 336, 481–489 (2018)",{"doi":274},{"id":502,"text":503,"url":504,"identifiers":505},"39893e34-a162-47ec-9c1d-391359122bbe","Zhang, J., Lou, Z., Ji, Y., Shao, W.: Ground state of Kirchhoff type fractional Schrödinger equations with critical growth. J. Math. Anal. Appl. 462(1), 57–83 (2018)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0022247X18300982",{"doi":506},"10.1016\u002Fj.jmaa.2018.01.060",{"id":270,"text":508,"url":272,"identifiers":509},"Wang, Y., Jiang, J.: Existence and nonexistence of positive solutions for the fractional coupled system involving generalized p-Laplacian. Adv. Differ. Equ. 2017(1), 337 (2017)",{"doi":274},{"id":270,"text":511,"url":272,"identifiers":512},"Feng, Q., Meng, F.: Traveling wave solutions for fractional partial differential equations arising in mathematical physics by an improved fractional Jacobi elliptic equation method. Math. Methods Appl. Sci. 40(10), 3676–3686 (2017)",{"doi":274},{"id":514,"text":515,"url":516,"identifiers":517},"389937a3-1f33-461d-b3e7-9a65ae4b8a3b","Hao, X.: Positive solution for singular fractional differential equations involving derivatives. Adv. Differ. Equ. 2016(1), 139 (2016)","https:\u002F\u002Fadvancesincontinuousanddiscretemodels.springeropen.com\u002Farticles\u002F10.1186\u002Fs13662-016-0865-8",{"doi":518},"10.1186\u002Fs13662-016-0865-8",{"id":270,"text":520,"url":272,"identifiers":521},"Diblík, J., Feckan, M., Pospíšil, M.: On the new control functions for linear discrete delay systems. SIAM J. Control Optim. 52(3), 1745–1760 (2014)",{"doi":274},{"id":270,"text":523,"url":272,"identifiers":524},"Diblík, J., Khusainov, D.Y., Baštinec, J., Sirenko, A.: Exponential stability of linear discrete systems with constant coefficients and single delay. Appl. Math. Lett. 51, 68–73 (2016)",{"doi":274},{"id":270,"text":526,"url":272,"identifiers":527},"Wang, T., Zhang, Y., Qiu, J., Gao, H.: Adaptive fuzzy backstepping control for a class of nonlinear systems with sampled and delayed measurements. IEEE Trans. Fuzzy Syst. 23(2), 302–312 (2015)",{"doi":274},{"id":270,"text":529,"url":272,"identifiers":530},"Wang, Y., Cao, L., Zhang, S., Hu, X., Yu, F.: Command filtered adaptive fuzzy backstepping control method of uncertain non-linear systems. IET Control Theory Appl. 10(10), 1134–1141 (2016)",{"doi":274},{"id":532,"text":533,"url":534,"identifiers":535},"3eb39249-6d73-40f2-9dcb-2315327f6a81","Sadek, U., Sarjaš, A., Chowdhury, A., Svečko, R.: Improved adaptive fuzzy backstepping control of a magnetic levitation system based on symbiotic organism search. Appl. Soft Comput. 56, 19–33 (2017)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS1568494617301229",{"doi":536},"10.1016\u002Fj.asoc.2017.02.032",{"id":270,"text":538,"url":272,"identifiers":539},"Zhai, D., Xi, C., An, L., Dong, J., Zhang, Q.: Prescribed performance switched adaptive dynamic surface control of switched nonlinear systems with average dwell time. IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1257–1269 (2017)",{"doi":274},{"id":18,"text":541,"url":18,"identifiers":542},"Singh, U.P., Jain, S., Singh, R., Parmar, M., Makwana, R., Kumare, J.: Dynamic surface control based ts-fuzzy model for a class of uncertain nonlinear systems. Int. J. Control Theory Appl. 9(2), 1333–1345 (2016)",{},{"id":270,"text":544,"url":272,"identifiers":545},"Uyen, H.T.T., Tuan, P.D., Van Tu, V., Quang, L., Minh, P.X.: Adaptive neural networks dynamic surface control algorithm for 3 dof surface ship. In: System Science and Engineering (ICSSE), 2017 International Conference on, pp. 71–76. IEEE (2017)",{"doi":274},{"id":270,"text":547,"url":272,"identifiers":548},"Semprun, K.A., Yan, L., Butt, W.A., Chen, P.C.: Dynamic surface control for a class of nonlinear feedback linearizable systems with actuator failures. IEEE Trans. Neural Netw. Learn. Syst. 28(9), 2209–2214 (2017)",{"doi":274},{"id":270,"text":550,"url":272,"identifiers":551},"Farrell, J., Sharma, M., Polycarpou, M.: Backstepping-based flight control with adaptive function approximation. J. Guid. Control Dyn. 28(6), 1089–1102 (2005)",{"doi":274},{"id":553,"text":554,"url":555,"identifiers":556},"d0300bd3-4ba0-4430-9d87-4ff3f92a0825","Pan, Y., Yu, H.: Dynamic surface control via singular perturbation analysis. Automatica 57, 29–33 (2015)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0005109815001442",{"doi":557},"10.1016\u002Fj.automatica.2015.03.033",{"id":270,"text":559,"url":272,"identifiers":560},"Ma, J., Zheng, Z., Li, P.: Adaptive dynamic surface control of a class of nonlinear systems with unknown direction control gains and input saturation. IEEE Trans. Cybern. 45(4), 728–741 (2015)",{"doi":274},{"id":270,"text":562,"url":272,"identifiers":563},"Zhang, X., Liu, L., Wu, Y.: The uniqueness of positive solution for a fractional order model of turbulent flow in a porous medium. Appl. Math. Lett. 37, 26–33 (2014)",{"doi":274},{"id":270,"text":565,"url":272,"identifiers":566},"Wang, J., Yuan, Y., Zhao, S.: Fractional factorial split-plot designs with two-and four-level factors containing clear effects. Commun. Stat., Theory Methods 44(4), 671–682 (2015)",{"doi":274},{"id":270,"text":568,"url":272,"identifiers":569},"Zhang, L., Zheng, Z.: Lyapunov type inequalities for the Riemann–Liouville fractional differential equations of higher order. Adv. Differ. Equ. 2017(1), 270 (2017)",{"doi":274},{"id":270,"text":571,"url":272,"identifiers":572},"Liu, H., Pan, Y., Li, S., Chen, Y.: Synchronization for fractional-order neural networks with full\u002Funder-actuation using fractional-order sliding mode control. Int. J. Mach. Learn. Cybern. 9(7), 1219–1232 (2018)",{"doi":274},{"id":270,"text":574,"url":272,"identifiers":575},"Liu, H., Li, S., Li, G., Wang, H.: Adaptive controller design for a class of uncertain fractional-order nonlinear systems: an adaptive fuzzy approach. Int. J. 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Asian-Eur. J. Math. 1, 131-146 (2008)",{"doi":670},"10.1142\u002FS179355710800014X",{"id":18,"text":672,"url":18,"identifiers":673},"Bahaa, GM: Optimality conditions for infinite order distributed parabolic systems with multiple time delays given in integral form. J. Appl. Math. 2012, 672947 (2012)",{},{"id":18,"text":675,"url":18,"identifiers":676},"Bahaa, GM, Kotarski, W: Time-optimal control of infinite order distributed parabolic systems involving multiple time-varying lags. Numer. Funct. Anal. Optim. 37(9), 1066-1088 (2016)",{"doi":677},"10.1080\u002F01630563.2016.1186693",{"id":18,"text":679,"url":18,"identifiers":680},"Bahaa, GM, Tharwat, MM: Optimal boundary control for infinite variables parabolic systems with time lags given in integral form. Iran. J. Sci. Technol. 3, 277-291 (2012)",{},{"id":18,"text":682,"url":18,"identifiers":683},"Lions, JL: Optimal Control of Systems Governed by Partial Differential Equations, Band 170. Springer, Berlin (1971)",{"doi":684},"10.1007\u002F978-3-642-65024-6",{"id":18,"text":686,"url":18,"identifiers":687},"Lions, JL, Magenes, E: Non-Homogeneous Boundary Value Problem and Applications, vol. I. Springer, New York (1972)",{},{"id":18,"text":689,"url":18,"identifiers":690},"Kotarski, W, El-Saify, HA, Bahaa, GM: Optimal control of parabolic equation with an infinite number of variables for non-standard functional and time delay. IMA J. Math. Control Inf. 19, 461-476 (2002)",{"doi":691},"10.1093\u002Fimamci\u002F19.4.461",{"id":18,"text":693,"url":18,"identifiers":694},"Agrawal, OP: Formulation of Euler-Lagrange equations for fractional variational problems. J. Math. Anal. Appl. 272, 368-379 (2002)",{"doi":695},"10.1016\u002FS0022-247X(02)00180-4",{"id":18,"text":697,"url":18,"identifiers":698},"Agrawal, OP: A general formulation and solution scheme for fractional optimal control problems. Nonlinear Dyn. 38, 323-337 (2004)",{"doi":699},"10.1007\u002Fs11071-004-3764-6",{"id":18,"text":701,"url":18,"identifiers":702},"Agrawal, OP: Fractional optimal control of a distributed system using eigenfunctions. J. Comput. Nonlinear Dyn. 3(2), 1-6 (2008)",{"doi":703},"10.1115\u002F1.2833873",{"id":18,"text":705,"url":18,"identifiers":706},"Agrawal, OP, Baleanu, D: A Hamiltonian formulation and direct numerical scheme for fractional optimal control problems. J. Vib. Control 13(9-10), 1269-1281 (2007)",{"doi":707},"10.1177\u002F1077546307077467",{"id":18,"text":709,"url":18,"identifiers":710},"Agrawal, OP, Defterli, O, Baleanu, D: Fractional optimal control problems with several state and control variables. J. Vib. Control 16(13), 1967-1976 (2010)",{"doi":711},"10.1177\u002F1077546309353361",{"id":18,"text":713,"url":18,"identifiers":714},"Bahaa, GM: Fractional optimal control problem for variational inequalities with control constraints. IMA J. Math. Control Inf. 6(33), 1-16 (2016)",{},{"id":18,"text":716,"url":18,"identifiers":717},"Bahaa, GM: Fractional optimal control problem for differential system with control constraints. Filomat 30(8), 2177-2189 (2016)",{"doi":718},"10.2298\u002FFIL1608177B",{"id":18,"text":720,"url":18,"identifiers":721},"Bahaa, GM: Fractional optimal control problem for infinite order system with control constraints. Adv. Differ. Equ. 2016, 250 (2016)",{"doi":722},"10.1186\u002Fs13662-016-0976-2",{"id":18,"text":724,"url":18,"identifiers":725},"Baleanu, D, Muslih, SI: Lagrangian formulation on classical fields within Riemann-Liouville fractional derivatives. Phys. Scr. 72(2-3), 119-121 (2005)",{"doi":726},"10.1238\u002FPhysica.Regular.072a00119",{"id":18,"text":728,"url":18,"identifiers":729},"Baleanu, D, Avkar, T: Lagrangian with linear velocities within Riemann-Liouville fractional derivatives. Nuovo Cimento B 119, 73-79 (2004)",{},{"id":18,"text":731,"url":18,"identifiers":732},"Baleanu, DA, Agrawal, OP: Fractional Hamilton formalism within Caputo’s derivative. Czechoslov. J. Phys. 56(10\u002F11), 1087-1092 (2006)",{"doi":733},"10.1007\u002Fs10582-006-0406-x",{"id":18,"text":735,"url":18,"identifiers":736},"Baleanu, D, Defterli, O, Agrawal, OP: Central difference numerical scheme for fractional optimal control problems. J. Vib. Control 15(4), 583-597 (2009)",{"doi":737},"10.1177\u002F1077546308088565",{"id":18,"text":739,"url":18,"identifiers":740},"Frederico Gastao, F, Torres Delfim, FM: Fractional optimal control in the sense of Caputo and the fractional Noether’s theorem. Int. Math. Forum 3(10), 479-493 (2008)",{},{"id":18,"text":742,"url":18,"identifiers":743},"Jajarmi, A, Baleanu, D: Suboptimal control of fractional-order dynamic systems with delay argument. J. Vib. Control (2017). doi: 10.1177\u002F1077546316687936",{"doi":744},"10.1177\u002F1077546316687936",{"id":18,"text":746,"url":18,"identifiers":747},"Jarad, F, Maraba, T, Baleanu, D: Fractional variational optimal control problems with delayed arguments. Nonlinear Dyn. 62, 609-614 (2010)",{"doi":748},"10.1007\u002Fs11071-010-9748-9",{"id":18,"text":750,"url":18,"identifiers":751},"Jarad, F, Maraba, T, Baleanu, D: Higher order fractional variational optimal control problems with delayed arguments. Appl. Math. Comput. 218, 9234-9240 (2012)",{},{"id":18,"text":753,"url":18,"identifiers":754},"Mophou, GM: Optimal control of fractional diffusion equation. Comput. Math. Appl. 61, 68-78 (2011)",{"doi":755},"10.1016\u002Fj.camwa.2010.10.030",{"id":18,"text":757,"url":18,"identifiers":758},"Mophou, GM: Optimal control of fractional diffusion equation with state constraints. Comput. Math. Appl. 62, 1413-1426 (2011)",{"doi":759},"10.1016\u002Fj.camwa.2011.04.044",{"id":18,"text":761,"url":18,"identifiers":762},"Mophou, GM, Fotsing, JM: Optimal control of a fractional diffusion equation with delay. J. Adv. Math. 6(3), 1017-1037 (2014)",{},{"id":18,"text":764,"url":18,"identifiers":765},"Oldham, KB, Spanier, J: The Fractional Calculus. Academic Press, New York (1974)",{},{"id":18,"text":767,"url":18,"identifiers":768},"Defterli, O, D’Elia, M, Du, Q, Gunzburger, M, Lehoucq, R, Meerschaert, MM: Fractional diffusion on bounded domains. Fract. Calc. Appl. Anal. 18(2), 342-360 (2015)",{"doi":769},"10.1515\u002Ffca-2015-0023",{"id":18,"text":771,"url":18,"identifiers":772},"Doha, EH, Bhrawy, AH, Baleanu, D, Ezz-Eldien, SS, Hafez, RM: An efficient numerical scheme based on the shifted orthonormal Jacobi polynomials for solving fractional optimal control problems. Adv. Differ. Equ. 2015, 15 (2015)",{},{"id":18,"text":774,"url":18,"identifiers":775},"Podlubny, I: Fractional Differential Equations. Academic Press, San Diego (1999)",{},{"id":777,"createTime":778,"updateTime":779,"relativeEntities":780,"slug":781,"properties":782,"entityType":161,"verifyStatus":162,"verifyTime":793,"verifyNote":164,"languages":18,"translateLanguages":18,"viewCount":19,"primaryUrl":794,"fullTextUrl":18,"authors":795,"publicationType":214,"publisherRelationship":847,"citationCount":19,"citationInfo":890,"publishDate":893,"publishYear":891,"citationAnalyzeStatus":390,"lastCitationAnalyze":779,"indexDatabases":894,"openAccess":18,"references":18,"isForceReanalyzing":309},"69f4b12c-dd25-42ed-8165-ae769cd05af5","2023-12-01T23:31:25.832+00:00","2026-07-24T03:55:23.671+00:00",[],"Dynamics-of-a-two-dimensional-competitive-system-of-rational-difference-equations-with-quadratic-terms",{"abstract":783,"title":785,"gsPaper":787,"references":789,"doi":791},{"EN":784},"We investigate global dynamics of the following systems of difference equations: \n                \n                  \n                    \n                  \n                \n               where the parameters \n                \n                    \n                  \n              , \n                \n                    \n                  \n              , \n                \n                    \n                  \n              , \n                \n                    \n                  \n               are positive numbers and the initial condition \n                \n                    \n                  \n               is an arbitrary nonnegative number and \n                \n                    \n                  \n               is a positive number. We show that this system has rich dynamics which depends on the part of a parametric space. We find precisely the basins of attraction of all attractors including the points at ∞. MSC:39A10, 39A30, 37E99, 37D10.",{"EN":786},"Dynamics of a two-dimensional competitive system of rational difference equations with quadratic terms",{"VOID":788},"[\"10328768934190939671\"]",{"VOID":790},"Garić-Demirović M, Kulenović MRS, Nurkanović M: Global behavior of four competitive rational systems of difference equations in the plane. Discrete Dyn. Nat. Soc. 2009., 2009: Article ID 153058\nKulenović MRS, Merino O: Global bifurcation for competitive systems in the plane. Discrete Contin. Dyn. Syst., Ser. B 2009, 12: 133-149.\nKulenović MRS, Merino O: Invariant manifolds for competitive discrete systems in the plane. Int. J. Bifurc. Chaos Appl. Sci. Eng. 2010, 20: 2471-2486. 10.1142\u002FS0218127410027118\nBurgić D, Kulenović MRS, Nurkanović M: Global dynamics of a rational system of difference equations in the plane. Commun. Appl. Nonlinear Anal. 2008, 15: 71-84.\nClark D, Kulenović MRS, Selgrade JF: Global asymptotic behavior of a two dimensional difference equation modelling competition. Nonlinear Anal. TMA 2003, 52: 1765-1776. 10.1016\u002FS0362-546X(02)00294-8\nCushing JM, Levarge S, Chitnis N, Henson SM: Some discrete competition models and the competitive exclusion principle. J. Differ. Equ. Appl. 2004, 10: 1139-1152. 10.1080\u002F10236190410001652739\nHirsch M, Smith H: Monotone dynamical systems. II. In Handbook of Differential Equations: Ordinary Differential Equations. Elsevier, Amsterdam; 2005:239-357.\nKulenović MRS, Merino O: Discrete Dynamical Systems and Difference Equations with Mathematica. Chapman & Hall\u002FCRC, Boca Raton; 2002.\nKulenović MRS, Merino O: Competitive-exclusion versus competitive-coexistence for systems in the plane. Discrete Contin. Dyn. Syst., Ser. B 2006, 6: 1141-1156.\nKulenović MRS, Nurkanović M: Asymptotic behavior of a linear fractional system of difference equations. J. Inequal. Appl. 2005, 2005: 127-143.\nLeonard WJ, May R: Nonlinear aspects of competition between species. SIAM J. Appl. Math. 1975, 29: 243-275. 10.1137\u002F0129022\nSmith HL: Periodic competitive differential equations and the discrete dynamics of competitive maps. J. Differ. Equ. 1986, 64: 165-194. 10.1016\u002F0022-0396(86)90086-0\nSmith HL: Periodic solutions of periodic competitive and cooperative systems. SIAM J. Math. Anal. 1986, 17: 1289-1318. 10.1137\u002F0517091\nSmith HL: Planar competitive and cooperative difference equations. J. Differ. Equ. Appl. 1998, 3: 335-357. 10.1080\u002F10236199708808108\nBrett A, Kulenović MRS: Basins of attraction of equilibrium points of monotone difference equations. Sarajevo J. Math. 2009, 5: 211-233.\nBurgić D, Kalabušić S, Kulenović MRS: Nonhyperbolic dynamics for competitive systems in the plane and global period-doubling bifurcations. Adv. Dyn. Syst. Appl. 2008, 3: 229-249.\nCamouzis E, Kulenović MRS, Ladas G, Merino O: Rational systems in the plane. J. Differ. Equ. Appl. 2009, 15: 303-323. 10.1080\u002F10236190802125264\nClark D, Kulenović MRS: On a coupled system of rational difference equations. Comput. Math. Appl. 2002, 43: 849-867. 10.1016\u002FS0898-1221(01)00326-1\nde Mottoni P, Schiaffino A: Competition systems with periodic coefficients: a geometric approach. J. Math. Biol. 1981, 11: 319-335. 10.1007\u002FBF00276900\nFranke JE, Yakubu A-A: Mutual exclusion verses coexistence for discrete competitive systems. J. Math. Biol. 1991, 30: 161-168. 10.1007\u002FBF00160333\nFranke JE, Yakubu A-A: Geometry of exclusion principles in discrete systems. J. Math. Anal. Appl. 1992, 168: 385-400. 10.1016\u002F0022-247X(92)90167-C\nKalabušić S, Kulenović MRS, Pilav E: Multiple attractors for a competitive system of rational difference equations in the plane. Abstr. Appl. Anal. 2011., 2011: Article ID 295308\nKalabušić S, Kulenović MRS, Pilav E: Dynamics of a two-dimensional system of rational difference equations of Leslie-Gower type. Adv. Differ. Equ. 2011., 2011: Article ID 29\nKulenović MRS, Ladas G: Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures. Chapman & Hall\u002FCRC, Boca Raton; 2001.\nHess P Pitman Research Notes in Mathematics Series 247. In Periodic-Parabolic Boundary Value Problems and Positivity. Longman Scientific & Technical, Harlow; 1991. viii+139 pp.\nYang L, Hou X, Zeng Z: Complete discrimination system for polynomials. Sci. China Ser. E 1996, 39(6):628-646.\nBasu S, Merino O: On the behavior of solutions of a system of difference equations. Commun. Appl. Nonlinear Anal. 2009, 16(1):89-101.\nWalker RJ: Algebraic Curves. Princeton University Press, Princeton; 1950.\nGelfand IM, Kapranov MM, Zelevinsky AV: Discriminants, Resultants and Multidimensional Determinants. Birkhäuser, Boston; 1994.",{"VOID":792},"10.1186\u002F1687-1847-2014-301","2024-08-30T20:31:04.135+00:00","https:\u002F\u002Fadvancesindifferenceequations.springeropen.com\u002Farticles\u002F10.1186\u002F1687-1847-2014-301",[796,813,830],{"id":797,"sortIndex":19,"researcher":18,"roles":798,"affiliations":799,"properties":808,"displayName":810,"givenName":18,"familyName":18},"cb739120-a1f7-42e8-b8e3-09b65db68ed4",[170],[800],{"id":801,"sortIndex":19,"affiliation":802,"properties":18},"f605f878-9525-4596-a86e-ad62e2df3cde",{"id":801,"createTime":18,"updateTime":18,"relativeEntities":803,"slug":18,"properties":804,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":807,"statistic":18},[],{"title":805},{"VI":806},"Division of Mathematics, Faculty of Mechanical Engineering, University of Sarajevo, Sarajevo, Bosnia and Herzegovina",[],{"title":809,"gsAuthor":811},{"VI":810},"Vahidin 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this paper, we study the solution of impulsive fractional differential equations with multiple delays by using the nonlinear alternative of Leray–Schauder and the Banach fixed point method. Also, we prove that the equations have at least one solution or unique solution with certain conditions. In the last part, we give two examples to illustrate the usefulness of the main results.",{"EN":905},"Existence results for fractional order impulsive functional differential equations with multiple delays",{"VOID":907},"[\"8569464588563011511\"]",{"VOID":909},"10.1186\u002Fs13662-018-1580-4","2024-04-30T06:43:44.226+00:00","https:\u002F\u002Fadvancesindifferenceequations.springeropen.com\u002Farticles\u002F10.1186\u002Fs13662-018-1580-4",[913,928],{"id":914,"sortIndex":19,"researcher":18,"roles":915,"affiliations":916,"properties":925,"displayName":927,"givenName":18,"familyName":18},"efcc450a-9379-45a7-9a00-fed2086d1606",[170],[917],{"id":918,"sortIndex":19,"affiliation":919,"properties":18},"2eac04ed-eafd-4c04-acce-5d531580147c",{"id":918,"createTime":18,"updateTime":18,"relativeEntities":920,"slug":18,"properties":921,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":924,"statistic":18},[],{"title":922},{"VI":923},"School of Mathematics and Statistics, Huangshan University, Huangshan, P.R. 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Academic Press, San Diego (1999)",{"doi":274},{"id":270,"text":997,"url":272,"identifiers":998},"Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York (1993)",{"doi":274},{"id":1000,"text":1001,"url":1002,"identifiers":1003},"7ecb2f65-8a2b-4e0b-81be-a974d1fe8212","Kosmatov, N.: Integral equations and initial value problems for nonlinear differential equations of fractional order. Nonlinear Anal. 70, 2521–2529 (2009)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0362546X08002447",{"doi":1004},"10.1016\u002Fj.na.2008.03.037",{"id":18,"text":1006,"url":18,"identifiers":1007},"Zhang, S.Q.: Existence of solution for a boundary value problem of fractional order. Acta Math. Sci. 26, 220–228 (2006)",{},{"id":270,"text":1009,"url":272,"identifiers":1010},"Lv, Z.W., Liang, J., Xiao, T.J.: Solutions to fractional differential equations with nonlocal initial condition in Banach spaces. Adv. Differ. Equ. 2010, Article ID 340349 (2010)",{"doi":274},{"id":270,"text":1012,"url":272,"identifiers":1013},"Goodrich, C.S.: Existence of a positive solution to systems of differential equations of fractional order. Comput. Math. Appl. 62, 1251–1268 (2011)",{"doi":274},{"id":1015,"text":1016,"url":1017,"identifiers":1018},"7baa43e5-35f4-4cad-aacc-ec6a0449b63e","Yang, X., Wei, Z.L., Dong, W.: Existence of positive solutions for the boundary value problem of nonlinear fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 17, 85–92 (2012)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS1007570411002334",{"doi":1019},"10.1016\u002Fj.cnsns.2011.05.007",{"id":1021,"text":1022,"url":1023,"identifiers":1024},"1ac53ec0-4146-4148-9631-de232587c335","Tang, X.S.: Existence of solutions of four-point boundary value problems for fractional differential equations at resonance. J. Appl. Math. Comput. 51, 145–160 (2016)","http:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs12190-015-0896-4",{"doi":1025},"10.1007\u002Fs12190-015-0896-4",{"id":270,"text":1027,"url":272,"identifiers":1028},"Zhou, Y.: Existence and uniqueness of fractional functional differential equations with unbounded delay. Int. J. Dyn. Syst. Differ. Equ. 1, 239–244 (2008)",{"doi":274},{"id":1030,"text":1031,"url":1032,"identifiers":1033},"5da424c7-7c4a-48f3-99d8-cbe08eea1f95","Zhou, Y., Jiao, F., Li, J.: Existence and uniqueness for fractional neutral differential equations with infinite delay. Nonlinear Anal. 71, 3249–3256 (2009)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0362546X09002338",{"doi":1034},"10.1016\u002Fj.na.2009.01.202",{"id":270,"text":1036,"url":272,"identifiers":1037},"Ouahab, A.: Local and global existence and uniqueness results for impulsive functional differential equations with multiple delay. J. Math. Anal. Appl. 323, 456–472 (2006)",{"doi":274},{"id":18,"text":1039,"url":18,"identifiers":1040},"Darwish, M.A., Ntouyas, S.K.: Functional differential equations of fractional order with state-dependent delay. Dyn. Syst. Appl. 18, 539–550 (2009)",{},{"id":270,"text":1042,"url":272,"identifiers":1043},"Fec̃kan, M., Zhou, Y., Wang, J.R.: On the concept and existence of solution for impulsive fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 17, 3050–3060 (2012)",{"doi":274},{"id":270,"text":1045,"url":272,"identifiers":1046},"Wang, J.R., Fec̃kan, M., Zhou, Y.: On the new concept of solutions and existence results for impulsive fractional evolution equations. Dyn. Partial Differ. Equ. 8, 345–361 (2011)",{"doi":274},{"id":270,"text":1048,"url":272,"identifiers":1049},"Shu, X.B., Lai, Y.Z., Chen, Y.M.: The existence of mild solutions for impulsive fractional partial differential equations. Nonlinear Anal. TMA 74, 2003–2011 (2011)",{"doi":274},{"id":270,"text":1051,"url":272,"identifiers":1052},"Chen, A., Chen, Y.: Existence of solutions to anti-periodic boundary value problem for nonlinear fractional differential equations with impulses. Adv. Differ. Equ. 2011, Article ID 915689 (2011)",{"doi":274},{"id":1054,"text":1055,"url":1056,"identifiers":1057},"5a4a3042-0c98-474b-a5ee-b0c95405b642","Jiang, H.P.: Existence results for fractional order functional differential equations with impulse. Comput. Math. Appl. 64, 3477–3483 (2012)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0898122112001812",{"doi":1058},"10.1016\u002Fj.camwa.2012.02.056",{"id":270,"text":1060,"url":272,"identifiers":1061},"Shu, X.B., Shi, Y.J.: A study on the mild solution of impulsive fractional evolution equations. Appl. Math. Comput. 15, 465–476 (2016)",{"doi":274},{"id":1063,"createTime":1064,"updateTime":1065,"relativeEntities":1066,"slug":1067,"properties":1068,"entityType":161,"verifyStatus":162,"verifyTime":1079,"verifyNote":164,"languages":18,"translateLanguages":18,"viewCount":19,"primaryUrl":1080,"fullTextUrl":18,"authors":1081,"publicationType":214,"publisherRelationship":1097,"citationCount":19,"citationInfo":1140,"publishDate":1143,"publishYear":1141,"citationAnalyzeStatus":17,"lastCitationAnalyze":1144,"indexDatabases":1145,"openAccess":18,"references":18,"isForceReanalyzing":309},"cba10824-faa4-499b-8109-d93bbf02c5f0","2023-12-11T17:43:51.941+00:00","2026-07-23T10:44:52.559+00:00",[],"Oscillatory-properties-of-half-linear-difference-equations-two-term-perturbations",{"abstract":1069,"title":1071,"gsPaper":1073,"references":1075,"doi":1077},{"EN":1070},"We consider the nonoscillatory half-linear difference equation \n                \n                  \n                    \n                  \n                  \n                    \n                  \n                \n               and we study the influence of the perturbations \n                  \n                    \n                  \n                  \n                    \n                  \n                , \n                  \n                    \n                  \n                  \n                    \n                  \n                 on the oscillatory properties of the equation \n                \n                  \n                    \n                  \n                  \n                    \n                  \n                \n               The presented oscillation and nonoscillation criteria are obtained using the variational principle and the so-called modified Riccati technique.",{"EN":1072},"Oscillatory properties of half-linear difference equations: two-term perturbations",{"VOID":1074},"[\"13151353749694257128\"]",{"VOID":1076},"Řehák P: Oscillatory properties of second order half-linear difference equations. Czechoslovak Math J 2001, 51: 303–321. 10.1023\u002FA:1013790713905\nAgarwal RP, Bohner M, Grace SR, O'Regan D: Discrete Oscillation Theory. Hindawi Publishing Corporation, New York; 2005.\nDošlý O, Řehák P: Half-Linear Differential Equations. In North-Holland Mathematics Studies. Volume 202. Elsevier, Amsterdam; 2005.\nDošlý O, Fišnarová S: Linearized Riccati technique and (non)oscillation criteria for half-linear difference equations. Adv Differ Equ 2008, 2008: 18. Article ID 438130\nDošlý O, Řehák P: Recessive solution of half-linear second order difference equations. J Differ Equ Appl 2003, 9: 49–61.\nDošlý O, Fišnarová S: Half-linear oscillation criteria: Perturbation in term involving derivative. Nonlinear Anal Theory Methods Appl 2010, 73: 3756–3766. 10.1016\u002Fj.na.2010.07.049\nDošlý O, Fišnarová S: Variational technique and principal solution in half-linear oscillation criteria. Appl Math Comput 2011, 217: 5385–5391. 10.1016\u002Fj.amc.2010.12.006\nDošlý O: Oscillation criteria for higher order Sturm-Liouville difference equations. J Differ Equ Appl 1998, 4: 425–450. 10.1080\u002F10236199808808154\nErbe LH, Zhang BG: Oscillation of second order linear difference equations. Chin J Math 1988, 16: 239–252.\nDošlý O, Fišnarová S: Summation characterization of the recessive solution for half-linear second order difference equations. Adv Differ Equ 2009, 2009: 16. Article ID 521058",{"VOID":1078},"10.1186\u002F1687-1847-2012-101","2024-05-16T23:38:05.061+00:00","https:\u002F\u002Fadvancesindifferenceequations.springeropen.com\u002Farticles\u002F10.1186\u002F1687-1847-2012-101",[1082],{"id":1083,"sortIndex":19,"researcher":18,"roles":1084,"affiliations":1085,"properties":1094,"displayName":1096,"givenName":18,"familyName":18},"36a13e1d-8641-4f99-8f75-49e17df5f812",[170],[1086],{"id":1087,"sortIndex":19,"affiliation":1088,"properties":18},"55a3c3bd-6ea8-4219-a9f7-eeb116c6c82d",{"id":1087,"createTime":18,"updateTime":18,"relativeEntities":1089,"slug":18,"properties":1090,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1093,"statistic":18},[],{"title":1091},{"VI":1092},"Department of Mathematics, Mendel University in Brno, Brno, Czech Republic",[],{"title":1095},{"VI":1096},"Simona Fišnarová",{"url":1080,"publisher":1098,"properties":1135},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":1099,"slug":10,"properties":1100,"entityType":16,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":19,"subjectFields":1103,"manageAffiliations":1116,"indexDatabases":1122,"url":18,"thumbnailPath":18,"statistic":1130,"gsStatistic":18,"type":18,"analyzePriority":18},[],{"title":1101,"eissn":1102},{"EN":13},{"VOID":15},[1104,1108,1112],{"id":22,"createTime":18,"updateTime":18,"relativeEntities":1105,"label":1106,"description":1107,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":25},{},{"id":28,"createTime":18,"updateTime":18,"relativeEntities":1109,"label":1110,"description":1111,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":31},{},{"id":34,"createTime":18,"updateTime":18,"relativeEntities":1113,"label":1114,"description":1115,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":37},{},[1117],{"id":41,"createTime":18,"updateTime":18,"relativeEntities":1118,"slug":18,"properties":1119,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1121,"statistic":18},[],{"title":1120},{"EN":45},[],[1123],{"id":49,"indexDatabase":1124,"url":60,"indexYears":61,"academicFieldIds":1129,"indexDatabaseRanking":66},{"id":51,"createTime":18,"updateTime":18,"relativeEntities":1125,"label":1126,"description":1127,"key":57,"publicationTags":1128,"standard":18},[],{"EN":54,"VI":54},{"EN":54,"VI":56},[59],[63,64,65],{"impactFactor":19,"impactFactorByYear":1131,"i10Index":80,"i10IndexLast5Year":81,"totalPublication":82,"totalPublicationByYear":1132,"totalCitation":102,"totalCitationByYear":1133,"totalCitationPerPublication":121,"totalCitationPerPublicationByYear":1134,"hindexLast5Year":141,"hindex":141},{"2012":69,"2013":70,"2014":71,"2015":72,"2016":70,"2017":73,"2018":74,"2019":75,"2020":76,"2021":77,"2022":78,"2023":79},{"2004":84,"2005":85,"2006":86,"2007":87,"2008":88,"2009":89,"2010":90,"2011":91,"2012":92,"2013":93,"2014":94,"2015":95,"2016":96,"2017":97,"2018":98,"2019":99,"2020":100,"2021":101},{"2004":89,"2005":104,"2006":105,"2007":106,"2008":107,"2009":108,"2010":109,"2011":110,"2012":111,"2013":112,"2014":113,"2015":114,"2016":115,"2017":116,"2018":117,"2019":118,"2020":119,"2021":120},{"2004":123,"2005":124,"2006":125,"2007":126,"2008":127,"2009":128,"2010":129,"2011":130,"2012":131,"2013":132,"2014":133,"2015":134,"2016":135,"2017":136,"2018":137,"2019":138,"2020":139,"2021":140},{"pages":1136,"volume":1138},{"VOID":1137},"1-16",{"VOID":1139},"2012",{"total":19,"publishYear":1141,"statisticByYear":1142},2012,{},"2012-07-05","2026-07-23T10:44:52.558+00:00",[66],{"id":1147,"createTime":1148,"updateTime":1149,"relativeEntities":1150,"slug":1151,"properties":1152,"entityType":161,"verifyStatus":162,"verifyTime":1163,"verifyNote":164,"languages":18,"translateLanguages":18,"viewCount":19,"primaryUrl":1164,"fullTextUrl":18,"authors":1165,"publicationType":214,"publisherRelationship":1216,"citationCount":19,"citationInfo":1259,"publishDate":1262,"publishYear":1260,"citationAnalyzeStatus":390,"lastCitationAnalyze":1263,"indexDatabases":1264,"openAccess":18,"references":18,"isForceReanalyzing":309},"ab1605ba-1193-4404-810b-94c053c714e8","2024-01-15T16:05:27.516+00:00","2026-07-23T10:09:03.123+00:00",[],"Existence-results-for-fractional-neutral-functional-integro-differential-evolution-equations-with-infinite-delay-in-Banach-spaces",{"abstract":1153,"title":1155,"gsPaper":1157,"references":1159,"doi":1161},{"EN":1154},"In this paper, we investigate the existence results for a class of abstract fractional neutral integro-differential evolution systems involving the Caputo derivative in Banach spaces. The main techniques rely on the fractional calculus, properties of characteristic solution operators, Mönch’s fixed point theorem via measures of noncompactness. Particularly, we do not assume that characteristic solution operators are compact. The application is given to illustrate the theory. The results of this article are generalization and improvement of the recent results on this issue. MSC:26A33, 34A12, 47H08, 47H10.",{"EN":1156},"Existence results for fractional neutral functional integro-differential evolution equations with infinite delay in Banach spaces",{"VOID":1158},"[\"6435671842561579131\"]",{"VOID":1160},"Kilbas A, Srivastava H, Trujillo JJ: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam; 2006.\nLakshmikantham V, Leela S, Vasundhara Devi J: Theory of Fractional Dynamic Systems. Cambridge Scientific Publishers, Cambridge; 2009.\nMiller KS, Ross B: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York; 1993.\nPodlubny I: Fractional Differential Equations. Academic Press, New York; 1999.\nBaleanu D, Gunvenc ZB, Machdo JAT: New Trends in Nanotechnology and Fractional Calculus Applications. Springer, Berlin; 2010.\nBaleanu D, Diethelm K, Scalas E, Trujillo JJ Series on Complexity, Nonlinearity and Chaos. In Fractional Calculus Models and Numerical Methods. World Scientific, Singapore; 2012.\nBaleanu D, Tenreiro Machado JA, Luo ACJ: Fractional Dynamics and Control. Springer, Berlin; 2012.\nWu GC, Baleanu D: Variational iteration method for the Burgers’ flow with fractional derivatives-new Lagrange multipliers. Appl. Math. Model. 2013, 37(9):6183-6190. 10.1016\u002Fj.apm.2012.12.018\nBaleanu D, Mustafa OG, Agarwal RP:On L ( p ) - solutions for a class of sequential fractional differential equations. Appl. Math. Comput. 2011, 218(5):2074-2081. 10.1016\u002Fj.amc.2011.07.024\nHernández E, O’Regan D, Balachandran K: On recent developments in the theory of abstract differential equations with fractional derivatives. Nonlinear Anal. 2010, 73: 3462-3471. 10.1016\u002Fj.na.2010.07.035\nZhou Y, Jiao F: Existence of mild solutions for fractional neutral evolution equations. Comput. Math. Appl. 2010, 59: 1063-1077. 10.1016\u002Fj.camwa.2009.06.026\nZhou Y, Jiao F, Li J: Existence and uniqueness for fractional neutral differential equations with infinite delay. Nonlinear Anal. 2009, 71: 3249-3256. 10.1016\u002Fj.na.2009.01.202\nBaleanu D, Mustafa OG: On the global existence of solutions to a class of fractional differential equations. Comput. Math. Appl. 2010, 59(5):1835-1841. 10.1016\u002Fj.camwa.2009.08.028\nBaleanu D, Mustafa OG, Agarwal RP: An existence result for a superlinear fractional differential equation. Appl. Math. Lett. 2010, 23(9):1129-1132. 10.1016\u002Fj.aml.2010.04.049\ndos Santos JPC, Arjunan MM, Cuevas C: Existence results for fractional neutral integro-differential equations with state dependent delay. Comput. Math. Appl. 2011, 62(3):1275-1283. 10.1016\u002Fj.camwa.2011.03.048\ndos Santos JPC, Vijayakumar V, Murugesu R: Existence of mild solutions for nonlocal Cauchy problem for fractional neutral integro-differential equation with unbounded delay. Commun. Math. Anal. 2013, 14(1):59-71.\nJi S, Li G, Wang M: Controllability of impulsive differential systems with nonlocal conditions. Appl. Math. Comput. 2011, 217: 6981-6989. 10.1016\u002Fj.amc.2011.01.107\nWang JR, Fan Z, Zhou Y: Nonlocal controllability of semilinear dynamic systems with fractional derivative in Banach spaces. J. Optim. Theory Appl. 2012, 154(1):292-302. 10.1007\u002Fs10957-012-9999-3\nPazy A: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, New York; 1983.\nYan B: Boundary value problems on the half-line with impulses and infinite delay. J. Math. Anal. Appl. 2001, 259(1):94-114. 10.1006\u002Fjmaa.2000.7392\nKamenskii M, Obukhovskii V, Zecca P: Condensing Multivalued Maps and Semilinear Differential Inclusions in Banach Spaces. de Gruyter, Berlin; 2001.\nO’Regan D, Precup R: Existence criteria for integral equations in Banach spaces. J. Inequal. Appl. 2001, 6: 77-97.\nMönch H: Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces. Nonlinear Anal. 1980, 4: 985-999. 10.1016\u002F0362-546X(80)90010-3\nBanas J, Goebel K Lecture Notes in Pure and Applied Mathematics. In Measure of Noncompactness in Banach Spaces. Marcel Dekker, New York; 1980.",{"VOID":1162},"10.1186\u002F1687-1847-2013-215","2024-06-24T22:30:14.652+00:00","https:\u002F\u002Fadvancesincontinuousanddiscretemodels.springeropen.com\u002Farticles\u002F10.1186\u002F1687-1847-2013-215",[1166,1183],{"id":1167,"sortIndex":19,"researcher":18,"roles":1168,"affiliations":1169,"properties":1178,"displayName":1180,"givenName":18,"familyName":18},"94ce2bc8-5b75-45b6-8a80-7136328fa59a",[170],[1170],{"id":1171,"sortIndex":19,"affiliation":1172,"properties":18},"0e65265b-6dd3-43bb-9aeb-49d389609fda",{"id":1171,"createTime":18,"updateTime":18,"relativeEntities":1173,"slug":18,"properties":1174,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1177,"statistic":18},[],{"title":1175},{"VI":1176},"Department of Mathematics, RVS Faculty of Engineering, Coimbatore, India",[],{"title":1179,"gsAuthor":1181},{"VI":1180},"Chokkalingam Ravichandran",{"VOID":1182},"[\"BSR0U4sAAAAJ\"]",{"id":1184,"sortIndex":185,"researcher":18,"roles":1185,"affiliations":1186,"properties":1211,"displayName":1213,"givenName":18,"familyName":18},"305ae8dd-a6cc-40c2-a0ee-3663877a358d",[170],[1187,1195,1203],{"id":1188,"sortIndex":19,"affiliation":1189,"properties":18},"f6885131-1570-44ba-911a-42a602794c7f",{"id":1188,"createTime":18,"updateTime":18,"relativeEntities":1190,"slug":18,"properties":1191,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1194,"statistic":18},[],{"title":1192},{"VI":1193},"Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Cankaya University, Ankara, Turkey",[],{"id":1196,"sortIndex":185,"affiliation":1197,"properties":18},"2a5a48fd-87b4-4466-820a-9e2b5942493f",{"id":1196,"createTime":18,"updateTime":18,"relativeEntities":1198,"slug":18,"properties":1199,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1202,"statistic":18},[],{"title":1200},{"VI":1201},"Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia",[],{"id":1204,"sortIndex":130,"affiliation":1205,"properties":18},"1096e9c0-7290-4d86-887a-3dfa58133852",{"id":1204,"createTime":18,"updateTime":18,"relativeEntities":1206,"slug":18,"properties":1207,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1210,"statistic":18},[],{"title":1208},{"VI":1209},"Institute of Space Sciences, Magurele-Bucharest, Romania",[],{"title":1212,"gsAuthor":1214},{"VI":1213},"Dumitru Baleanu",{"VOID":1215},"[\"EFO9iO4AAAAJ\"]",{"url":1164,"publisher":1217,"properties":1254},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":1218,"slug":10,"properties":1219,"entityType":16,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":19,"subjectFields":1222,"manageAffiliations":1235,"indexDatabases":1241,"url":18,"thumbnailPath":18,"statistic":1249,"gsStatistic":18,"type":18,"analyzePriority":18},[],{"title":1220,"eissn":1221},{"EN":13},{"VOID":15},[1223,1227,1231],{"id":22,"createTime":18,"updateTime":18,"relativeEntities":1224,"label":1225,"description":1226,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":25},{},{"id":28,"createTime":18,"updateTime":18,"relativeEntities":1228,"label":1229,"description":1230,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":31},{},{"id":34,"createTime":18,"updateTime":18,"relativeEntities":1232,"label":1233,"description":1234,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":37},{},[1236],{"id":41,"createTime":18,"updateTime":18,"relativeEntities":1237,"slug":18,"properties":1238,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1240,"statistic":18},[],{"title":1239},{"EN":45},[],[1242],{"id":49,"indexDatabase":1243,"url":60,"indexYears":61,"academicFieldIds":1248,"indexDatabaseRanking":66},{"id":51,"createTime":18,"updateTime":18,"relativeEntities":1244,"label":1245,"description":1246,"key":57,"publicationTags":1247,"standard":18},[],{"EN":54,"VI":54},{"EN":54,"VI":56},[59],[63,64,65],{"impactFactor":19,"impactFactorByYear":1250,"i10Index":80,"i10IndexLast5Year":81,"totalPublication":82,"totalPublicationByYear":1251,"totalCitation":102,"totalCitationByYear":1252,"totalCitationPerPublication":121,"totalCitationPerPublicationByYear":1253,"hindexLast5Year":141,"hindex":141},{"2012":69,"2013":70,"2014":71,"2015":72,"2016":70,"2017":73,"2018":74,"2019":75,"2020":76,"2021":77,"2022":78,"2023":79},{"2004":84,"2005":85,"2006":86,"2007":87,"2008":88,"2009":89,"2010":90,"2011":91,"2012":92,"2013":93,"2014":94,"2015":95,"2016":96,"2017":97,"2018":98,"2019":99,"2020":100,"2021":101},{"2004":89,"2005":104,"2006":105,"2007":106,"2008":107,"2009":108,"2010":109,"2011":110,"2012":111,"2013":112,"2014":113,"2015":114,"2016":115,"2017":116,"2018":117,"2019":118,"2020":119,"2021":120},{"2004":123,"2005":124,"2006":125,"2007":126,"2008":127,"2009":128,"2010":129,"2011":130,"2012":131,"2013":132,"2014":133,"2015":134,"2016":135,"2017":136,"2018":137,"2019":138,"2020":139,"2021":140},{"pages":1255,"volume":1257},{"VOID":1256},"1-12",{"VOID":1258},"2013",{"total":19,"publishYear":1260,"statisticByYear":1261},2013,{},"2013-07-15","2026-07-23T10:09:03.121+00:00",[66],{"id":1266,"createTime":1267,"updateTime":1268,"relativeEntities":1269,"slug":1270,"properties":1271,"entityType":161,"verifyStatus":162,"verifyTime":1282,"verifyNote":164,"languages":18,"translateLanguages":18,"viewCount":19,"primaryUrl":1283,"fullTextUrl":18,"authors":1284,"publicationType":214,"publisherRelationship":1325,"citationCount":88,"citationInfo":1367,"publishDate":1369,"publishYear":661,"citationAnalyzeStatus":390,"lastCitationAnalyze":1370,"indexDatabases":1371,"openAccess":18,"references":18,"isForceReanalyzing":309},"79e6e478-859a-4461-8109-e37aa0298df7","2024-01-23T11:33:41.486+00:00","2026-07-23T10:06:50.810+00:00",[],"A-new-spline-in-compression-method-of-order-four-in-space-and-two-in-time-based-on-half-step-grid-points-for-the-solution-of-the-system-of-1D-quasi-linear-hyperbolic-partial-differential-equations",{"abstract":1272,"title":1274,"gsPaper":1276,"references":1278,"doi":1280},{"EN":1273},"In this paper, we propose a new three-level implicit method based on a half-step spline in compression method of order two in time and order four in space for the solution of one-space dimensional quasi-linear hyperbolic partial differential equation of the form \n                  \n                    \n                  \n                  \n                    \n                  \n                  $u_{tt} =A(x,t,u)u_{xx} +f(x,t,u,u_{x},u_{t})$\n                . We describe spline in compression approximations and their properties using two half-step grid points. The new method for one-dimensional quasi-linear hyperbolic equation is obtained directly from the consistency condition. In this method we use three grid points for the unknown function \n                  \n                    \n                  \n                  \n                    \n                  \n                  $u(x,t)$\n                 and two half-step points for the known variable ‘x’ in x-direction. The proposed method, when applied to a linear test equation, is shown to be unconditionally stable. We have also established the stability condition to solve a linear fourth-order hyperbolic partial differential equation. Our method is directly applicable to solve hyperbolic equations irrespective of the coordinate system, which is the main advantage of our work. The proposed method for a scalar equation is extended to solve the system of quasi-linear hyperbolic equations. To assess the validity and accuracy, the proposed method is applied to solve several benchmark problems, and numerical results are provided to demonstrate the usefulness of the proposed method.",{"EN":1275},"A new spline in compression method of order four in space and two in time based on half-step grid points for the solution of the system of 1D quasi-linear hyperbolic partial differential equations",{"VOID":1277},"[\"2860581345985391169\"]",{"VOID":1279},"Li, WD, Zhao, L: An analysis for a high order difference scheme for numerical solution to \\(u_{tt} = A(x, t)u_{xx} + f(x, t, u, u_{x}, u_{t})\\). Numer. Methods Partial Differ. Equ. 23, 484-498 (2007)\nBickley, WG: Piecewise cubic interpolation and two-point boundary value problems. Comput. J. 11, 206-208 (1968)\nFyfe, DJ: The use of cubic splines in the solution of two-point boundary value problems. Comput. J. 12, 188-192 (1969)\nPapamichael, N, Whiteman, JR: A cubic spline technique for the one-dimensional heat conduction equation. J. Inst. Math. Appl. 11, 111-113 (1973)\nRaggett, GF, Wilson, PD: A fully implicit finite difference approximation to the one-dimensional wave equation using a cubic spline technique. J. Inst. Math. Appl. 14, 75-77 (1974)\nFleck, JA Jr.: A cubic spline method for solving the wave equation of nonlinear optics. J. Comput. Phys. 16, 324-341 (1974)\nJain, MK, Aziz, T: Spline function approximation for differential equation. Comput. Methods Appl. Mech. Eng. 26, 129-143 (1981)\nJain, MK, Aziz, T: Cubic spline solution of two-point boundary value problems with significant first derivatives. Comput. Methods Appl. Mech. Eng. 39, 83-91 (1983)\nJain, MK, Iyengar, SRK, Pillai, ACR: Difference schemes based on splines in compression for the solution of conservation laws. Comput. Methods Appl. Mech. Eng. 38, 137-151 (1983)\nKadalbajoo, MK, Patidar, KC: Numerical solution of singularly perturbed two point boundary value problems by spline in compression. Int. J. Comput. Math. 77, 263-284 (2001)\nKadalbajoo, MK, Patidar, KC: Numerical solution of singularly perturbed two-point boundary value problems by spline in tension. Appl. Math. Comput. 131, 299-320 (2002)\nKhan, A, Aziz, T: Parametric cubic spline approach to the solution of a system of second order boundary value problems. J. Optim. Theory Appl. 118, 45-54 (2003)\nKadalbajoo, MK, Aggarwal, VK: Cubic spline for solving singular two-point boundary value problems. Appl. Math. Comput. 156, 249-259 (2004)\nMohanty, RK, Jha, N, Evans, DJ: Spline in compression method for the numerical solution of singularly perturbed two point singular boundary value problems. Int. J. Comput. Math. 81, 615-627 (2004)\nMohanty, RK, Evans, DJ, Arora, U: Convergence spline in tension methods for singularly perturbed two point singular boundary value problems. Int. J. Comput. Math. 82, 55-66 (2005)\nMohanty, RK, Jha, N: A class of variable mesh spline in compression methods for singularly perturbed two point single boundary value problems. Appl. Math. Comput. 168, 704-716 (2005)\nMohanty, RK, Arora, U: A family of non-uniform mesh tension spline methods for singularly perturbed two-point singular boundary value problems with significant first derivatives. Appl. Math. Comput. 172, 531-544 (2006)\nRashidinia, J, Jalilian, R, Kazemi, V: Spline methods for the solutions of hyperbolic equations. Appl. Math. Comput. 190, 882-886 (2007)\nRashidinia, J, Mohammadi, R: Non polynomial cubic spline methods for the solution of parabolic equations. Int. J. Comput. Math. 85, 843-850 (2008)\nSiraj-ul-Islam, Tirmizi, SIA: Nonpolynomial spline approach to the solution of a system of second order boundary value problems. Appl. Math. Comput. 173, 1208-1218 (2006)\nSiraj-ul-Islam, Tirmizi, SIA, Asharaf, S: A class of methods based on nonpolynomial spline functions for the solution of special fourth order boundary value problems with engineering applications. Appl. Math. Comput. 174, 1169-1180 (2006)\nDing, H, Zhang, Y: Parametric spline methods for the solution of hyperbolic equations. Appl. Math. Comput. 204, 938-941 (2008)\nMohanty, RK, Jain, MK: High accuracy cubic spline alternating group explicit methods for 1D quasilinear parabolic equations. Int. J. Comput. Math. 86, 1556-1571 (2009)\nMohanty, RK, Gopal, V: A fourth-order finite difference method based on spline in tension approximation for the solution of one-space dimensional second-order quasilinear hyperbolic equations. Adv. Differ. Equ. 2013, Article ID 70 (2013)\nMohanty, RK, Jha, N, Kumar, R: A new variable mesh method based on non-polynomial spline in compression approximations for 1D quasilinear hyperbolic equations. Adv. Differ. Equ. 2015, Article ID 337 (2015)\nMohanty, RK, Singh, S: High accuracy Numerov type discretization for the solution of one dimensional non-linear wave equation with variable coefficients. J. Adv. Res. Sci. Comput. 3(1), 53-66 (2011)\nMohanty, RK, Gopal, V: An off-step discretization for the solution of 1-D mildly non-linear wave equations with variable coefficients. J. Adv. Res. Sci. Comput. 4(2), 1-13 (2012)\nMohanty, RK, Jain, MK, George, K: On the use of high order difference methods for the system of one space second order non-linear hyperbolic equations with variable coefficients. J. Comput. Appl. Math. 72, 421-431 (1996)\nMohanty, RK, Arora, U: A new discretization method of order four for the numerical solution of one space dimensional second order quasi-linear hyperbolic equation. Int. J. Math. Educ. Sci. Technol. 33, 829-838 (2002)\nMohanty, RK, Gopal, V: High accuracy cubic spline difference approximation for the solution of one-space dimensional non-linear wave equations. Appl. Math. Comput. 218, 4234-4244 (2011)\nGopal, V, Mohanty, RK, Jha, N: New nonpolynomial spline in compression method of \\(\\mathrm{O}(\\mathrm{k}^{2} +\\mathrm {h}^{4})\\) for the solution of 1D wave equation in polar coordinates. Adv. Numer. Anal. 2013, Article ID 470480 (2013)\nMohanty, RK: Stability interval for explicit difference schemes for multi-dimensional second order hyperbolic equations with significant first order space derivative terms. Appl. Math. Comput. 190, 1683-1690 (2007)\nMohanty, RK: An unconditionally stable difference scheme for the one-space-dimensional linear hyperbolic equation. Appl. Math. Lett. 17, 101-105 (2004)\nMohanty, RK: New unconditionally stable difference schemes for the solution of multi-dimensional telegraph equations. Int. J. Comput. Math. 86, 2061-2071 (2009)\nMohanty, RK, Gopal, V: High accuracy non-polynomial spline in compression method for one-space dimensional quasi-linear hyperbolic equations with significant first order space derivative term. Appl. Math. Comput. 238, 250-265 (2014)\nMohanty, RK, Khurana, G: A new fast numerical method based on off-step discretization for two-dimensional quasilinear hyperbolic partial differential equations. Int. J. Comput. Methods (2016). doi:10.1142\u002FS0219876217500311\nMohanty, RK, Setia, N: A new high accuracy two-level implicit off-step discretization for the system of two space dimensional quasi-linear parabolic partial differential equations. Appl. Math. Comput. 219, 2680-2697 (2012)\nMohanty, RK, Jain, MK, Dhall, D: High accuracy cubic spline approximation for two dimensional quasi-linear elliptic boundary value problems. Appl. Math. Model. 37, 155-171 (2013)\nMohanty, RK, Gopal, V: A new off-step high order approximation for the solution of three-space dimensional nonlinear wave equations. Appl. Math. Model. 37, 2802-2815 (2013)\nMohanty, RK, Setia, N: A new high order compact off-step discretization for the system of 3D quasi-linear elliptic partial differential equations. Appl. Math. Model. 37, 6870-6883 (2013)\nMohanty, RK, Setia, N: A new compact high order off-step discretization for the system of 2D quasi-linear elliptic partial differential equations. Adv. Differ. Equ. 2013, Article ID 223 (2013)\nMohanty, RK, Singh, S, Singh, S: A new high order space derivative discretization for 3D quasi-linear hyperbolic partial differential equations. Appl. Math. Comput. 232, 529-541 (2014)\nMohanty, RK, Kumar, R: A new fast algorithm based on half-step discretization for one space dimensional quasi-linear hyperbolic equations. Appl. Math. Comput. 244, 624-641 (2014)\nMohanty, RK, Kumar, R: A novel numerical algorithm of Numerov type for 2D quasi-linear elliptic boundary value problems. Int. J. Comput. Methods Eng. Sci. Mech. 15, 473-489 (2014)\nMohanty, RK, Setia, N: A new high accuracy two-level implicit off-step discretization for the system of three space dimensional quasi-linear parabolic partial differential equations. Comput. Math. Appl. 69, 1096-1113 (2015)\nVarga, RS: Matrix Iterative Analysis, 2nd edn. Springer, Berlin (2000)\nHageman, LA, Young, DM: Applied Iterative Methods. Dover, New York (2004)\nKelly, CT: Iterative Methods for Linear and Non-linear Equations. SIAM, Philadelphia (1995)",{"VOID":1281},"10.1186\u002Fs13662-017-1147-9","2024-05-16T23:57:15.504+00:00","https:\u002F\u002Fadvancesincontinuousanddiscretemodels.springeropen.com\u002Farticles\u002F10.1186\u002Fs13662-017-1147-9",[1285,1302],{"id":1286,"sortIndex":19,"researcher":18,"roles":1287,"affiliations":1288,"properties":1297,"displayName":1299,"givenName":18,"familyName":18},"2ba84a76-9103-4be7-83c9-d9376c7789c0",[170],[1289],{"id":1290,"sortIndex":19,"affiliation":1291,"properties":18},"4ad836d7-6b2e-4802-ad44-cf668c12358b",{"id":1290,"createTime":18,"updateTime":18,"relativeEntities":1292,"slug":18,"properties":1293,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1296,"statistic":18},[],{"title":1294},{"VI":1295},"Department of Applied Mathematics, South Asian University, New Delhi, India",[],{"title":1298,"gsAuthor":1300},{"VI":1299},"RK Mohanty",{"VOID":1301},"[\"e3wM6PwAAAAJ\"]",{"id":1303,"sortIndex":185,"researcher":18,"roles":1304,"affiliations":1305,"properties":1320,"displayName":1322,"givenName":18,"familyName":18},"72f60208-246e-4e6c-9c4f-64da8540f8a3",[170],[1306,1312],{"id":1290,"sortIndex":19,"affiliation":1307,"properties":18},{"id":1290,"createTime":18,"updateTime":18,"relativeEntities":1308,"slug":18,"properties":1309,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1311,"statistic":18},[],{"title":1310},{"VI":1295},[],{"id":1313,"sortIndex":185,"affiliation":1314,"properties":18},"d05515f5-5d48-4574-a642-da001c11874e",{"id":1313,"createTime":18,"updateTime":18,"relativeEntities":1315,"slug":18,"properties":1316,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1319,"statistic":18},[],{"title":1317},{"VI":1318},"Department of Mathematics, I.P. College for Women, University of Delhi, Delhi, India",[],{"title":1321,"gsAuthor":1323},{"VI":1322},"Gunjan Khurana",{"VOID":1324},"[\"hAj4XzEAAAAJ\"]",{"url":1283,"publisher":1326,"properties":1363},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":1327,"slug":10,"properties":1328,"entityType":16,"verifyStatus":17,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":19,"subjectFields":1331,"manageAffiliations":1344,"indexDatabases":1350,"url":18,"thumbnailPath":18,"statistic":1358,"gsStatistic":18,"type":18,"analyzePriority":18},[],{"title":1329,"eissn":1330},{"EN":13},{"VOID":15},[1332,1336,1340],{"id":22,"createTime":18,"updateTime":18,"relativeEntities":1333,"label":1334,"description":1335,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":25},{},{"id":28,"createTime":18,"updateTime":18,"relativeEntities":1337,"label":1338,"description":1339,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":31},{},{"id":34,"createTime":18,"updateTime":18,"relativeEntities":1341,"label":1342,"description":1343,"parentId":18,"standard":18,"scholarHubFieldId":18},[],{"EN":37},{},[1345],{"id":41,"createTime":18,"updateTime":18,"relativeEntities":1346,"slug":18,"properties":1347,"entityType":18,"verifyStatus":18,"verifyTime":18,"verifyNote":18,"languages":18,"translateLanguages":18,"viewCount":18,"url":18,"parentIds":1349,"statistic":18},[],{"title":1348},{"EN":45},[],[1351],{"id":49,"indexDatabase":1352,"url":60,"indexYears":61,"academicFieldIds":1357,"indexDatabaseRanking":66},{"id":51,"createTime":18,"updateTime":18,"relativeEntities":1353,"label":1354,"description":1355,"key":57,"publicationTags":1356,"standard":18},[],{"EN":54,"VI":54},{"EN":54,"VI":56},[59],[63,64,65],{"impactFactor":19,"impactFactorByYear":1359,"i10Index":80,"i10IndexLast5Year":81,"totalPublication":82,"totalPublicationByYear":1360,"totalCitation":102,"totalCitationByYear":1361,"totalCitationPerPublication":121,"totalCitationPerPublicationByYear":1362,"hindexLast5Year":141,"hindex":141},{"2012":69,"2013":70,"2014":71,"2015":72,"2016":70,"2017":73,"2018":74,"2019":75,"2020":76,"2021":77,"2022":78,"2023":79},{"2004":84,"2005":85,"2006":86,"2007":87,"2008":88,"2009":89,"2010":90,"2011":91,"2012":92,"2013":93,"2014":94,"2015":95,"2016":96,"2017":97,"2018":98,"2019":99,"2020":100,"2021":101},{"2004":89,"2005":104,"2006":105,"2007":106,"2008":107,"2009":108,"2010":109,"2011":110,"2012":111,"2013":112,"2014":113,"2015":114,"2016":115,"2017":116,"2018":117,"2019":118,"2020":119,"2021":120},{"2004":123,"2005":124,"2006":125,"2007":126,"2008":127,"2009":128,"2010":129,"2011":130,"2012":131,"2013":132,"2014":133,"2015":134,"2016":135,"2017":136,"2018":137,"2019":138,"2020":139,"2021":140},{"pages":1364,"volume":1366},{"VOID":1365},"1-28",{"VOID":659},{"total":88,"publishYear":661,"statisticByYear":1368},{},"2017-03-29","2026-07-23T10:06:50.809+00:00",[66],{"id":1373,"createTime":1374,"updateTime":1375,"relativeEntities":1376,"slug":1377,"properties":1378,"entityType":161,"verifyStatus":162,"verifyTime":1389,"verifyNote":164,"languages":18,"translateLanguages":18,"viewCount":19,"primaryUrl":1390,"fullTextUrl":18,"authors":1391,"publicationType":214,"publisherRelationship":1424,"citationCount":1466,"citationInfo":1467,"publishDate":1476,"publishYear":891,"citationAnalyzeStatus":17,"lastCitationAnalyze":1477,"indexDatabases":1478,"openAccess":18,"references":18,"isForceReanalyzing":309},"039aea18-4bfe-4d7e-80d5-ff2e3561449f","2024-01-26T18:43:17.012+00:00","2026-07-22T20:46:39.225+00:00",[],"The-modified-Kudryashov-method-for-solving-some-fractional-order-nonlinear-equations",{"abstract":1379,"title":1381,"gsPaper":1383,"references":1385,"doi":1387},{"EN":1380},"In this paper, the modified Kudryashov method is proposed to solve fractional differential equations, and Jumarie’s modified Riemann-Liouville derivative is used to convert nonlinear partial fractional differential equation to nonlinear ordinary differential equations. The modified Kudryashov method is applied to compute an approximation to the solutions of the space-time fractional modified Benjamin-Bona-Mahony equation and the space-time fractional potential Kadomtsev-Petviashvili equation. As a result, many analytical exact solutions are obtained including symmetrical Fibonacci function solutions, hyperbolic function solutions, and rational solutions. This method is powerful, efficient, and it can be used as an alternative to establish new solutions of different types of fractional differential equations applied in mathematical physics.",{"EN":1382},"The modified Kudryashov method for solving some fractional-order nonlinear equations",{"VOID":1384},"[\"4936199498854929986\"]",{"VOID":1386},"Zhang S: Application of Exp-function method to a KdV equation with variable coefficients. Phys. Lett. A 2007, 365: 448–453. 10.1016\u002Fj.physleta.2007.02.004\nMisirli E, Gurefe Y: Exp-function method to solve the generalized Burgers-Fisher equation. Nonlinear Sci. Lett. A 2010, 1: 323–328.\nMisirli E, Gurefe Y: Exp-function method for solving nonlinear evolution equations. Math. Comput. Appl. 2011, 16: 258–266.\nLiu S, Fu Z, Liu S, Zhao Q: Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Phys. Lett. A 2001, 289: 69–74. 10.1016\u002FS0375-9601(01)00580-1\nYan Z:Abundant families of Jacobi elliptic function solutions of the (2+1) -dimensional integrable Davey-Stewartson-type equation via a new method. Chaos Solitons Fractals 2003, 18: 299–309. 10.1016\u002FS0960-0779(02)00653-7\nTascan F, Bekir A, Koparan M: Travelling wave solutions of nonlinear evolution equations by using the first integral method. Commun. Nonlinear Sci. Numer. Simul. 2009, 10: 1810–1815.\nAbbasbandy S, Shirzadi A: The first integral method for modified Benjamin-Bona-Mahony equation. Commun. Nonlinear Sci. Numer. Simul. 2010, 15: 1759–1765. 10.1016\u002Fj.cnsns.2009.08.003\nZayed EME, Gepreel KA:The ( G ′ \u002FG) -expansion method for finding traveling wave solutions of nonlinear partial differential equations in mathematical physics. J. Math. Phys. 2009., 50: Article ID 013502 10.1063\u002F1.3033750\nWanga M, Lia X, Zhanga J:The ( G ′ \u002FG) -expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Phys. Lett. A 2008, 372: 417–423. 10.1016\u002Fj.physleta.2007.07.051\nSoliman AA, Abdo HA: New exact solutions of nonlinear variants of the RLW, the PHI-four and Boussinesq equations based on modified extended direct algebraic method. Int. J. Nonlinear Sci. 2009, 7(3):274–282.\nSalas AH, Gomez CA: Application of the Cole-Hopf transformation for finding exact solutions to several forms of the seventh-order KdV equation. Math. Probl. Eng. 2010., 2010: Article ID 194329 10.1155\u002F2010\u002F194329\nPodlubny I Math. Sci. Eng. In Fractional Differential Equations. Academic Press, New York; 1999.\nBhrawy AH, Baleanu D: A spectral Legendre-Gauss-Labatto collacation method for a space-time fractional advection diffusion equations with variable coefficients. Rep. Math. Phys. 2013, 72: 219–233. 10.1016\u002FS0034-4877(14)60015-X\nJafari H, Nazari M, Baleanu D, Khalique CM: A new approach for solving a system of fractional partial differential equations. Comput. Math. Appl. 2013, 66: 838–843. 10.1016\u002Fj.camwa.2012.11.014\nMehdinejadiani B, Naseri AA, Jafari H, Ghanbarzadeh A, Baleanu D: A mathematical model for simulation of a water table profile between two parallel subsurface drains using fractional derivatives. Comput. Math. Appl. 2013, 66: 785–794. 10.1016\u002Fj.camwa.2013.01.002\nMomani S, Odibat Z, Erturk VS: Generalized differential transform method for solving a space- and time-fractional diffusion-wave equation. Phys. Lett. A 2007, 370: 379–387. 10.1016\u002Fj.physleta.2007.05.083\nEl-Sayed AMA, Behiry SH, Raslan WE: Adomian’s decomposition method for solving an intermediate fractional advection-dispersion equation. Int. J. Nonlinear Sci. 2010, 59: 1759–1765.\nHu Y, Luo Y, Lu Z: Analytical solution of the linear fractional differential equation by Adomian decomposition method. J. Comput. Appl. Math. 2008, 215: 220–229. 10.1016\u002Fj.cam.2007.04.005\nSaadatmandi A, Dehghan M: A new operational matrix for solving fractional-order differential equations. Comput. Math. Appl. 2010, 59: 1326–1336. 10.1016\u002Fj.camwa.2009.07.006\nInc M: The approximate and exact solutions of the space- and time-fractional Burgers equations with initial conditions by variational iteration method. J. Math. Anal. Appl. 2008, 345: 476–484. 10.1016\u002Fj.jmaa.2008.04.007\nWua G, Lee EWM: Fractional variational iteration method and its application. Phys. Lett. A 2010, 374: 2506–2509. 10.1016\u002Fj.physleta.2010.04.034\nElbeleze AA, Kilicman A, Taib BM: Fractional variational iteration method and its application to fractional partial differential equation. Math. Probl. Eng. 2013., 2013: Article ID 543848 10.1155\u002F2013\u002F543848\nZhang S, Zhang HQ: Fractional sub-equation method and its applications to nonlinear fractional PDEs. Phys. Lett. A 2011, 375: 1069–1073. 10.1016\u002Fj.physleta.2011.01.029\nMeng F, Feng Q: A new fractional sub-equation method and its applications for space-time fractional partial differential equations. J. Appl. Math. 2013., 2013: Article ID 481729 10.1155\u002F2013\u002F481729\nAlzaidy JF: Fractional sub-equation method and its applications to the space-time fractional differential equations in mathematical physics. Br. J. Math. Comput. Sci. 2013, 3: 153–163.\nAlzaidy JF: The fractional sub-equation method and exact analytical solutions for some nonlinear fractional PDEs. Am. J. Math. Anal. 2013, 11: 14–19.\nGuo S, Mei L, Li Y, Sun Y: The improved fractional sub-equation method and its applications to the space-time fractional differential equations in fluid mechanics. Phys. Lett. A 2012, 376: 407–411. 10.1016\u002Fj.physleta.2011.10.056\nZheng B: Exp-function method for solving fractional partial differential equations. Sci. World J. 2013., 2013: Article ID 465723 10.1155\u002F2013\u002F465723\nLu B: The first integral method for some time fractional differential equations. J. Math. Anal. Appl. 2012, 395: 684–693. 10.1016\u002Fj.jmaa.2012.05.066\nYounis M: The first integral method for time-space fractional differential equations. J. Adv. Phys. 2013, 2: 220–223. 10.1166\u002Fjap.2013.1074\nMeng F: A new approach for solving fractional partial differential equations. J. Appl. Math. 2013., 2013: Article ID 256823 10.1155\u002F2013\u002F256823\nZayed EME, Amer YA, Shohib RMA:Exact traveling wave solutions for nonlinear fractional partial differential equations using the improved ( G ′ \u002FG) -expansion method. Int. J. Eng. Appl. Sci. 2014, 7: 18–31.\nJumarie G: Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results. Comput. Math. Appl. 2006, 51: 1367–1376. 10.1016\u002Fj.camwa.2006.02.001\nJumarie G: Fractional partial differential equations and modified Riemann-Liouville derivative new methods for solution. J. Appl. Math. Comput. 2007, 24: 31–48. 10.1007\u002FBF02832299\nKudryashov NA: One method for finding exact solutions of nonlinear differential equations. Commun. Nonlinear Sci. Numer. Simul. 2012, 17: 2248–2253. 10.1016\u002Fj.cnsns.2011.10.016\nEge SM, Misirli E: The modified Kudryashov method for solving some evolution equations. AIP Conf. Proc. 2012, 1470: 244–246.\nEge SM, Misirli E: Solutions of the space-time fractional foam-drainage equation and the fractional Klein-Gordon equation by use of modified Kudryashov method. Int. J. Res. Advent Technol. 2014, 2(3):384–388.\nKabir MM: Modified Kudryashov method for generalized forms of the nonlinear heat conduction equation. Int. J. Phys. Sci. 2011, 6: 6061–6064.\nKabir MM, Khajeh A, Aghdam EA, Koma AY: Modified Kudryashov method for finding exact solitary wave solutions of higher-order nonlinear equations. Math. Methods Appl. Sci. 2011, 34: 244–246.\nStakhov A, Rozin B: On a new class of hyperbolic functions. 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Biophys J 1995, 68: 46–53. 10.1016\u002FS0006-3495(95)80157-8","https:\u002F\u002Fdoi.org\u002F10.1016\u002Fs0006-3495(95)80157-8",{"mag":1565,"pmc":1566,"openalex":1567,"pm":1568,"doi":1569},"2094706142","1281659","W2094706142","7711266","10.1016\u002Fs0006-3495(95)80157-8",{"id":18,"text":1571,"url":18,"identifiers":1572},"Hilfer R: Applications of Fractional Calculus in Physics. World Scientific, Singapore; 2000.",{},{"id":1574,"text":1575,"url":1576,"identifiers":1577},"c9c8031d-588a-454d-9b1f-a6b030bda361","Metzler F, Schick W, Kilian HG, Nonnenmacher TF: Relaxation in filled polymers: A fractional calculus approach. J Chem Phys 1995, 103: 7180–7186. 10.1063\u002F1.470346","https:\u002F\u002Fpubs.aip.org\u002Fjcp\u002Farticle\u002F103\u002F16\u002F7180\u002F480141\u002FRelaxation-in-filled-polymers-A-fractional",{"doi":1578},"10.1063\u002F1.470346",{"id":18,"text":1580,"url":18,"identifiers":1581},"Podlubny I: Fractional Differential Equations. Academic Press, San Diego; 1999.",{},{"id":270,"text":1583,"url":272,"identifiers":1584},"Poudlubny I: Geometric and physical interpretation of fractional integration and fractional differentiation. Fract Calc Appl Anal 2002, 5: 367–386.",{"doi":274},{"id":270,"text":1586,"url":272,"identifiers":1587},"Kilbas AA, Srivastava HM, Trujillo JJ: Theory and applications of fractional differential equations. In North-Holland Mathematics Studies. Volume 204. Elsevier Science B. V, Amesterdam; 2009.",{"doi":274},{"id":270,"text":1589,"url":272,"identifiers":1590},"Lashmikantham V, Leela S, Vasundhara J: Theory of fractional dynamic systems. Cambridge Academic Publishers, Cambridge; 2009.",{"doi":274},{"id":1592,"text":1593,"url":1594,"identifiers":1595},"be1c6b37-0a14-4a3b-bb5a-171aae7f3c91","Agarwal RP, Benchohra M, Hamani S: Asurvey on existence result for boundary value problems of nonlinear fractional differential equations and inclusions. 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Abstract and Applied Analysis 2009., 2009: Article ID 768920. doi: 10.1155\u002F2009\u002F768920","https:\u002F\u002Fonlinelibrary.wiley.com\u002Fdoi\u002F10.1155\u002F2009\u002F768920",{"doi":1608},"10.1155\u002F2009\u002F768920",{"id":270,"text":1610,"url":272,"identifiers":1611},"Babakhani A: Positive solutions for system of nonlinear fractional differential equations in two dimensions with delay. 2010., 2010:",{"doi":274},{"id":1613,"text":1614,"url":1615,"identifiers":1616},"80665789-430e-4e7c-8b1d-05826abf239d","Baleanu D, Golmankhaneh AK, Nigmatullin R: Fractional Newtonian mechanics. Central Eur J Phys 2010, 8: 120–125. 10.2478\u002Fs11534-009-0085-x","https:\u002F\u002Fwww.degruyter.com\u002Fdocument\u002Fdoi\u002F10.2478\u002Fs11534-009-0085-x\u002Fhtml",{"doi":1617},"10.2478\u002Fs11534-009-0085-x",{"id":1619,"text":1620,"url":1621,"identifiers":1622},"eae4a146-8aa3-4fff-9948-31479988939d","Baleanu D, Trujillo JJ: A new method of finding the fractional Euler-Lagrange and Hamilton equations within Caputo fractional derivatives. Commun Nonlinear Sci Numer Simul 2010, 15(5):111–115.","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS1007570409002573",{"doi":1623},"10.1016\u002Fj.cnsns.2009.05.023",{"id":270,"text":1625,"url":272,"identifiers":1626},"Baleanu D, Trujillo JJ: New applications of fractoinal variational principles. Rep Math Phys 2008, 61: 331–335.",{"doi":274},{"id":270,"text":1628,"url":272,"identifiers":1629},"Benchohra M, Hamani S, Ntouyas SK: Boundary value problems for differential equations with fractional order. Surv Math Appl 2008, 3: 1–12.",{"doi":274},{"id":1631,"text":1632,"url":1633,"identifiers":1634},"90721e00-33bc-4ca3-94e6-89490c3087a0","Baleanu D, Mustafa OG: On the global existence of solutions to a class of fractional differential equations. Comput Math Appl 2010, 59: 1835–1841. 10.1016\u002Fj.camwa.2009.08.028","https:\u002F\u002Flinkinghub.elsevier.com\u002Fretrieve\u002Fpii\u002FS0898122109005616",{"doi":1635},"10.1016\u002Fj.camwa.2009.08.028",{"id":1637,"text":1638,"url":1639,"identifiers":1640},"414fb851-d7df-45f8-908f-c9dac188344b","Chang YK, Nieto JJ: Some new existence results for fractional differential inclusions with boundary conditions. Math Comput Model 2009, 49: 605–609. 10.1016\u002Fj.mcm.2008.03.014","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0895717708001015",{"doi":1641},"10.1016\u002Fj.mcm.2008.03.014",{"id":1643,"text":1644,"url":1645,"identifiers":1646},"f5fc2c11-5318-466b-a72d-7c5fcdef872f","Ouahab A: Some results for fractional boundary value problem of differential inclusions. Nonlinear Anal 2008, 69(11):3877–3896. 10.1016\u002Fj.na.2007.10.021","https:\u002F\u002Flinkinghub.elsevier.com\u002Fretrieve\u002Fpii\u002FS0362546X07006967",{"doi":1647},"10.1016\u002Fj.na.2007.10.021",{"id":270,"text":1649,"url":272,"identifiers":1650},"Miller KB, Ross B: An introduction to the fractional calculus and fractional differential equations. Wiely, New York; 1993.",{"doi":274},{"id":270,"text":1652,"url":272,"identifiers":1653},"Samko SG, Kilbas AA, Marichev OI: Fractional integrals and derivatives: Theory and applications. Gordon and Breach, Yverdon; 1993.",{"doi":274},{"id":1655,"text":1656,"url":1657,"identifiers":1658},"d33a37eb-f927-47c7-b192-4e396787f577","Zhang S: Positive solutions to singular boundary value problem for nonlinear fractional differential equation. Comput Math Appl 2010, 59(3):1300–1309. 10.1016\u002Fj.camwa.2009.06.034","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0898122109004167",{"doi":1659},"10.1016\u002Fj.camwa.2009.06.034",{"id":18,"text":1661,"url":1662,"identifiers":1663},"Feng M, Liu X, Feng H: The existence of positive solution to a nonlinear fractional differential equation with integral boundary conditions. Adv Diff Equ 2011, 2011: 14. 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Article ID 720702, doi:10.1155\u002F2011\u002F720702 10.1186\u002F1687-2770-2011-20","https:\u002F\u002Fdoi.org\u002F10.1155\u002F2011\u002F720702",{"mag":1674,"openalex":1675,"doi":1676},"2027141800","W2027141800","10.1155\u002F2011\u002F720702",{"id":1678,"text":1679,"url":1680,"identifiers":1681},"22353506-9270-435f-9a82-506d99f967c1","Belarbi A, Benchohra M, Ouahab A: Uniqueness results for fractional differential equations with infinite delay in Frechet space. Appl Anal 2006, 85: 1459–1470. 10.1080\u002F00036810601066350","http:\u002F\u002Fwww.tandfonline.com\u002Fdoi\u002Fabs\u002F10.1080\u002F00036810601066350",{"doi":1682},"10.1080\u002F00036810601066350",{"id":1684,"text":1685,"url":1686,"identifiers":1687},"cc5cb4a1-537e-48de-9798-a641e8606e01","Benchohra M, Henderson J, Ntouyas SK, Ouahab A: Existence esults for fractional order functional differential equations. 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Nonlinear Anal TMA 2008, 69: 2677–2682. 10.1016\u002Fj.na.2007.08.042","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS0362546X07005834",{"doi":1700},"10.1016\u002Fj.na.2007.08.042"]