Giải pháp soliton và ảnh hưởng của bậc phân số lên soliton trong mô hình quang phi tuyến

Abazari, R.: The (G’/G)-expansion method for Tzitzéica type nonlinear evolution equations. Math. Comput. Model. 52(9–10), 1834–1845 (2010) Abdeljawad, T.: On conformable fractional calculus. J. Comput. Appl. Math. 279, 57–66 (2015) Ahmad, I., Ahmad, H., Inc, M., Rezazadeh, H., Akbar, M.A., Khater, M.M.A., Akinyemi, L., Jhangeer, A.: Solution of fractional-order Korteweg-de Vries and Burgers’ equations utilizing local meshless method. J. Ocean Eng. Sci. (2021). https://doi.org/10.1016/j.joes.2021.08.014 Akinyemi, L., Akpan, U., Veeresha, P., Rezazadeh, H., Inc, M.: Computational techniques to study the dynamics of generalized unstable nonlinear Schrödinger equation. J. Ocean Eng. Sci. (2022). https://doi.org/10.1016/j.joes.2022.02.011 Ala, V., Demirbilek, U., Mamedov, K.R.: On the exact solutions to conformable equal width wave equation by improved Bernoulli sub-equation function method. Bull. South Ural State Univ. Ser. Math. Mech. Phys. 13(3), 1–13 (2021) Ali, K.K., Yilmazer, R., Osman, M.S.: Dynamic behavior of the (3+1)-dimensional KdV-Calogero-Bogoyavlenskii-Schif equation. Opt. Quant. Electron. 54, 160 (2022) Aljoudi, S.: Exact solutions of the fractional Sharma-Tasso-Olver equation and the fractional Bogoyavlenskii’s breaking soliton equations. Appl. Math. Comput. 405, 126237 (2021) Almeida, R.: A Caputo fractional derivative of a function with respect to another function. Commun. Nonlin. Sci. Numer. Simulat. 44, 460–481 (2017) Altwaty, A.A., Hassan, S.M., Masry, B.R.: Optical solitons with fractional temporal evolution in fiber Bragg gratings with generalized anti-cubic nonlinearity by the fractional Riccati method. Results Phys. 22, 103872 (2021) Arqub, O.A., Al-Smadi, M., Almusawa, H., Baleanu, D., Hayat, T., Alhodaly, M., Osman, M.S.: A novel analytical algorithm for generalized fifth-order time-fractional nonlinear evolution equations with conformable time derivative arising in shallow water waves. Alex. Eng. J. 61, 5753–5769 (2022) Baskonus, H.M., Bulut, H.: On the complex structures of Kundu-Eckhaus equation via improved Bernoulli sub-equation function method. Waves Random Complex Media 25(4), 720–728 (2015) Borhanifar, A., Moghanlu, A.Z.: Application of the (G’/G)-expansion method for the Zhiber-Shabat equation and other related equations. Math. Comput. Model. 54(9–10), 2109–2116 (2011) Demirbilek, U., Ala, V., Mamedov, K.R.: Exact solutions of conformable time fractional Zoomeron equation via IBSEFM. Appl. Math. A J. Chin. Univ. 36(4), 554–563 (2021) Demirbileko, U., Ala, V., Mamedov, K.R.: An application of improved Bernoulli sub-equation function method to the nonlinear conformable time-fractional equation. Tbilisi Math. J. 14(3), 59–70 (2021) Ghanbari, B., Rada, L.: Solitary wave solutions to the Tzitzeica type equations obtained by a new efficient approach. J. Appl. Anal. Comput. 9(2), 568–589 (2019) Hosseini, K., Ayati, Z., Ansari, R.: New exact solutions of the Tzitzéica-type equations in non-linear optics using the exp a function method. J. Modern Opt. 65(7), 847–851 (2018) Ilhan, O.A., Baskonus, H.M., Islam, M.N., Akbar, M.A., Soybaş, D.: Stable soliton solutions to the time fractional evolution equations in mathematical physics via the new generalized -expansion method. J. Nonlinear Sci. Numer. Simul. Int (2021). https://doi.org/10.1515/ijnsns-2020-0153 Inan, B., Osman, M.S., Turgut, A., Baleanu, D.: Analytical and numerical solutions of mathematical biology models: the Newell–Whitehead–Segel and Allen-Cahn equations. Math. Met. Appl. Sci. 43(5), 2588–2600 (2020) Islam, M.N., Miah, M.M., Rahman, M.A., Akbar, M.A.: Adequate closed form wave solutions to the space-time fractional nonlinear equations in physical sciences. Partial Differ. Equ. Appl. Math. 3, 100024 (2021a) Islam, M.E., Kundu, P.R., Akbar, M.A., Gepreel, K.A., Alotaibi, H.: Study of the parametric effect of self-control waves of the Nizhnik–Novikov–Veselov equation by the analytical solutions. Results Phys. 22, 103887 (2021b) Islam, M.E., Barman, H.K., Akbar, M.A.: Stable soliton solutions to the nonlinear low-pass electrical transmission lines and the Cahn-Allen equation. Heliyon 7(5), e06910 (2021c) Jhangeer, A., Faridi, W.A., Asjad, M.I., Inc, M.: A comparative study about the propagation of water waves with fractional operators. J. Ocean Eng. Sci. (2022). https://doi.org/10.1016/j.joes.2022.02.010.(inpress) Jumarie, G.: Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results. Comput. Math. Appl. 51(9–10), 1367–1376 (2006) Khalid, A., Rehan, A., Nisar, K.S., Osman, M.S.: Splines solutions of boundary value problems that arises in sculpturing electrical process of motors with two rotating mechanism circuit. Phys. Scr. 96(10), 104001 (2021) Khalil, R., Al Horani, M., Yousef, A., Sababheh, M.: A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014) Khan, K., Akbar, M.A.: Exact and solitary wave solutions for the Tzitzeica–Dodd–Bullough and the modified KdV-Zakharov-Kuznetsov equations using the modified simple equation method. Ain Shams Eng. J. 4(4), 903–909 (2013) Khater, M.M.A., Jhangeer, A., Rezazadeh, H., Akinyemi, L., Akbar, M.A., Inc, M., Ahmad, H.: New kinds of analytical solitary wave solutions for ionic currents on microtubules equation via two different techniques. Opt. Quant. Electron. 53, 609 (2021) Khodadad, F.S., Mirhosseini-Alizamini, S.M., Günay, B., Akinyemi, L., Rezazadeh, H., Inc, M.: Abundant optical solitons to the Sasa-Satsuma higher-order nonlinear Schrödinger equation. Opt. Quant. Electron. 53, 702 (2021) Korkmaz, A., Hepson, O.E., Hosseini, K., Rezazadeh, H., Eslami, M.: Sine-Gordon expansion method for exact solutions to conformable time fractional equations in RLW-class. J. King Saud Univ. Sci. 32(1), 567–574 (2020) Kumar, D., Hosseini, K., Samadani, F.: The sine-Gordon expansion method to look for the traveling wave solutions of the Tzitzéica type equations in nonlinear optics. Optik 149, 439–446 (2017) Kumar, S., Dhiman, S.K., Baleanu, D., Osman, M.S., Wazwaz, A.M.: Lie symmetries, closed-form solutions, and various dynamical profiles of solitons for the variable coefficient (2+1)-dimensional KP equations. Symmetry 14, 597 (2022) Li, C., Guo, Q.: On the solutions of the space-time fractional coupled Jaulent-Miodek equation associated with energy-dependent Schrödinger potential. Appl. Math. Lett. 121, 107517 (2021) Liu, J.G., Zhu, W.H., Osman, M.S., Ma, W.X.: An explicit plethora of different classes of interactive lump solutions for an extension form of 3D-Jimbo-Miwa model. Eur. Phys. J. Plus 135, 412 (2020) Liu, H.Z., Zhu, G.Q.: Comment on “the solitons and periodic travelling wave solutions for Dodd-Bullough-Mikhailov and Tzitzeica-Dodd-Bullough equations in quantum field theory”, Optik 168, 807–816”. Optik, 203, 163870 (2018) Mamun, A.A., Shahen, N.H.M., Ananna, S.N., Asaduzzaman, M.: Solitary and periodic wave solutions to the family of new 3D fractional WBBM equations in mathematical physics. Heliyon 7(7), e07483 (2021) Miller, K.S., Ross, B.: An introduction to the fractional calculus and fractional differential equations. Wiley (1993) Nisar, K.S., Ilhan, O.A., Manafian, J., Shahriari, M., Soybaş, D.: Analytical behavior of the fractional Bogoyavlenskii equations with conformable derivative using two distinct reliable methods. Results Phys. 22, 103975 (2021) Nisar, K.S., Ciancio, A., Ali, K.K., Osman, M.S., Cattani, C., Baleanu, D., Zafar, A., Raheel, M., Azeem, M.: On beta-time fractional biological population model with abundant solitary wave structures. Alex. Eng. J. 61(3), 1996–2008 (2022) Park, C., Khater, M.M., Attia, R.A., Alharbi, W., Alodhaibi, S.S.: An explicit plethora of solution for the fractional nonlinear model of the low-pass electrical transmission lines via Atangana-Baleanu derivative operator. Alex. Eng. J. 59(3), 1205–1214 (2020) Raza, N., Rafiq, M.H., Kaplan, M., Kumar, S., Chu, Y.M.: The unified method for abundant soliton solutions of local time fractional nonlinear evolution equations. Results Phys. 22, 103979 (2021) Roy, R., Akbar, M.A., Seadawy, A.R., Baleanu, D.: Search for adequate closed form wave solutions to space-time fractional nonlinear equations. Partial Differ. Equ. Appl. Math. 3, 100025 (2021) Scherer, R., Kalla, S.L., Tang, Y., Huang, J.: The Grünwald-Letnikov method for fractional differential equations. Comput. Math. Appl. 62(3), 902–917 (2011) Scott, A.C., Chu, F.Y.F., McLaughlin, D.W.: The soliton: a new concept in applied science. Proc. IEEE 61(10), 1443–1483 (1973) Siddique, I., Jaradat, M.M.M., Zafar, A., Mehdi, K.B., Osman, M.S.: Exact traveling wave solutions for two prolific conformable M-Fractional differential equations via three diverse approaches. Results Phys. 28, 104557 (2021) Tariq, K.U., Tala-Tebue, E., Rezazadeh, H., Younis, M., Bekir, A., Chu, Y.M.: Construction of new exact solutions of the resonant fractional NLS equation with the extended Fan sub-equation method. J. King Saud Univ. Sci. 33(8), 101643 (2021) Tarla, S., Ali, K.K., Sun, T.C., Yilmazer, R., Osman, M.S.: Nonlinear pulse propagation for novel optical solitons modeled by Fokas system in monomode optical fibers. Results Phys. 36, 105381 (2022) Wang, K.J.: On the new exact traveling wave solutions of the time-space fractional strain wave equation in microstructured solids via the variational method. Commun. Theor. Phys. 73(4), 045001 (2021) Wazwaz, A.M.: The tanh method: solitons and periodic solutions for the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations. Chaos Solitons Fractals 25(1), 55–63 (2005) Wazwaz, A.M.: The tanh method for travelling wave solutions to the Zhiber-Shabat equation and other related equations. Commun. Nonlinear Sci. Numer. Simul. 13(3), 584–592 (2008) Yepez-Martinez, H., Gómez-Aguilar, J.F.: Optical solitons solution of resonance nonlinear Schrödinger type equation with Atangana’s-conformable derivative using sub-equation method. Waves Random Complex Media 31(3), 573–596 (2021) Yue, C., Elmoasry, A., Khater, M.M.A., Osman, M.S., Attia, R.A.M., Lu, D., Elazab, N.S.: On complex wave structures related to the nonlinear long-short wave interaction system: analytical and numerical techniques. AIP Adv. 10, 045212 (2020) Yue, C., Lu, D., Khater, M.: Abundant wave accurate analytical solutions of the fractional nonlinear Hirota–Satsuma–Shallow water wave equation. Fluids 6(7), 235 (2021) Zafar, A., Raheel, M., Zafar, M.Q., Nisar, K.S., Osman, M.S., Mohamed, R.N., Elfasakhany, A.: Dynamics of different nonlinearities to the perturbed nonlinear Schrödinger equation via solitary wave solutions with numerical simulation. Fract. Fract. 5, 213 (2021a) Zafar, A., Rezazadeh, H., Reazzaq, W., Bekir, A.: The simplest equation approach for solving nonlinear Tzitzéica type equations in nonlinear optics. Modern Phys. Lett. B 35(07), 2150132 (2021b) Zhou, J., Zhou, R., Zhu, S.: Peakon, rational function and periodic solutions for Tzitzeica–Dodd–Bullough type equations. Chaos Solitons Fractals 141, 110419 (2020)