Sự tồn tại và phân tích tiệm cận của các nghiệm dương cho một phương trình vi phân phân kỳ với điều kiện biên không địa phương

Heymans, N., Kitagawa, M.: Modelling “unusual” behaviour after strain reversal with hierarchical fractional models. Rheol. Acta 43, 383–389 (2004)

Wang, Y., Liu, L., Zhang, X., Wu, Y.: Positive solutions of an abstract fractional semipositone differential system model for bioprocesses of HIV infection. Appl. Math. Comput. 258, 312–324 (2015)

Zhang, X., Mao, C., Liu, L., Wu, Y.: Exact iterative solution for an abstract fractional dynamic system model for bioprocess. Qual. Theory Dyn. Syst. 16, 205–222 (2017)

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)

Zhang, X., Liu, L., Wu, Y., Wiwatanapataphee, B.: Nontrivial solutions for a fractional advection dispersion equation in anomalous diffusion. Appl. Math. Lett. 66, 1–8 (2017)

Zhang, X., Liu, L., Wu, Y.: Variational structure and multiple solutions for a fractional advection-dispersion equation. Comput. Math. Appl. 68, 1794–1805 (2014)

Zhu, B., Liu, L., Wu, Y.: Local and global existence of mild solutions for a class of nonlinear fractional reaction–diffusion equations with delay. Appl. Math. Lett. 61, 73–79 (2016)

Zhu, B., Liu, L., Wu, Y.: Local and global existence of mild solutions for a class of semilinear fractional integro-differential equations. Fract. Calc. Appl. Anal. 20(6), 1338–1355 (2017)

Heymans, N., Podlubny, I.: Physical interpretation of initial conditions for fractional differential equations with Riemann–Liouville fractional derivatives. Rheol. Acta 45, 765–771 (2006)

Atangana, A.: Fractal-fractional differentiation and integration: connecting fractal calculus and fractional calculus to predict complex system. Chaos Solitons Fractals 102, 396–406 (2017)

Benkhettou, N., Cruz, A., Torres, D.: A fractional calculus on arbitrary time scales: fractional differentiation and fractional integration. Signal Process. 107, 230–237 (2015)

Qin, H., Zuo, X., Liu, J., Liu, L.: Approximate controllability and optimal controls of fractional dynamical systems of order \(1< q<2\) in Banach spaces. Adv. Differ. Equ. 2015, 73 (2015)

Zhang, X., Liu, L., Wu, Y.: Existence results for multiple positive solutions of nonlinear higher order perturbed fractional differential equations with derivatives. Appl. Math. Comput. 19, 1420–1433 (2012)

Zhang, X., Liu, L., Wu, Y., Wiwatanapataphee, B.: The spectral analysis for a singular fractional differential equation with a signed measure. Appl. Math. Comput. 257, 252–263 (2015)

Wang, Y., Liu, L., Wu, Y.: Extremal solutions for p-Laplacian fractional integro-differential equation with integral conditions on infinite intervals via iterative computation. Adv. Differ. Equ. 2015, 24 (2015)

Guan, Y., Zhao, Z., Lin, X.: On the existence of solutions for impulsive fractional differential equations. Adv. Math. Phys. 2017, Article ID 1207456 (2017)

Jiang, J., Liu, L., Wu, Y.: Positive solutions to singular fractional differential system with coupled boundary conditions. Commun. Nonlinear Sci. Numer. Simul. 18, 3061–3074 (2013)

Hao, X., Wang, H.: Positive solutions of semipositone singular fractional differential systems with a parameter and integral boundary conditions. Open Math. 16(1), 581–596 (2018)

Zhang, X., Liu, L., Wu, Y., Cui, Y.: New result on the critical exponent for solution of an ordinary fractional differential problem. J. Funct. Spaces 2017, Article ID 3976469 (2017)

Wang, F., Yang, Y.: Quasi-synchronization for fractional-order delayed dynamical networks with heterogeneous nodes. Appl. Math. Comput. 339, 1–14 (2018)

Wu, J., Zhang, X., Liu, L., Wu, Y., Cui, Y.: The convergence analysis and error estimation for unique solution of a p-Laplacian fractional differential equation with singular decreasing nonlinearity. Bound. Value Probl. 2018, 82 (2018)

Zhang, X., Liu, L., Wu, Y., Lu, Y.: The iterative solutions of nonlinear fractional differential equations. Appl. Math. Comput. 219, 4680–4691 (2013)

Zhang, X., Liu, L., Wu, Y.: Multiple positive solutions of a singular fractional differential equation with negatively perturbed term, Math. Comput. Model. 55, 1263–1274 (2012)

Zhang, X., Liu, L., Wiwatanapataphee, B., Wu, Y.: The eigenvalue for a class of singular p-Laplacian fractional differential equations involving the Riemann–Stieltjes integral boundary condition. Appl. Math. Comput. 235, 412–422 (2014)

Zhang, X., Liu, L., Wu, Y.: The eigenvalue problem for a singular higher fractional differential equation involving fractional derivatives. Appl. Math. Comput. 218, 8526–8536 (2012)

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)

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, 3676–3686 (2017)

Ren, T., Li, S., Zhang, X., Liu, L.: Maximum and minimum solutions for a nonlocal p -Laplacian fractional differential system from eco-economical processes. Bound. Value Probl. 2017(1), 118 (2017)

Zhang, X., Wu, Y., Cui, Y.: Existence and nonexistence of blow-up solutions for a Schrödinger equation involving a nonlinear operator. Appl. Math. Lett. 82, 85–91 (2018)

Zhang, X., Liu, L., Wu, Y., Cui, Y.: The existence and nonexistence of entire large solutions for a quasilinear Schrödinger elliptic system by dual approach. J. Math. Anal. Appl. 464(2), 1089–1106 (2018)

Lin, X., Zhao, Z.: Iterative technique for a third-order differential equation with three-point nonlinear boundary value conditions. Electron. J. Qual. Theory Differ. Equ. 2016, 12 (2016)

Zhang, X., Liu, L., Wu, Y., Caccetta, L.: Entire large solutions for a class of Schrödinger systems with a nonlinear random operator. J. Math. Anal. Appl. 423, 1650–1659 (2015)

Zhang, X., Liu, L., Wu, Y.: The uniqueness of positive solution for a singular fractional differential system involving derivatives. Commun. Nonlinear Sci. Numer. Simul. 18, 1400–1409 (2013)

Mao, J., Zhao, Z., Wang, C.: The exact iterative solution of fractional differential equation with nonlocal boundary value conditions. J. Funct. Spaces 2018, Article ID 8346398 (2018)

Chen, H., Chen, H., Li, M.: A new simultaneous iterative method with a parameter for solving the extended split equality problem and the extended split equality fixed point problem. Numer. Algorithms 79(4), 1231–1256 (2018)

Wang, Y., Liu, L.: Positive solutions for a class of fractional 3-point boundary value problems at resonance. Adv. Differ. Equ. 2017, 7 (2017)

Sun, F., Liu, L., Zhang, X., Wu, Y.: Spectral analysis for a singular differential system with integral boundary conditions. Mediterr. J. Math. 13, 4763–4782 (2016)

Liu, L., Sun, F., Zhang, X., Wu, Y.: Bifurcation analysis for a singular differential system with two parameters via to topological degree theory. Nonlinear Anal., Model. Control 22, 31–50 (2017)

Hao, X., Zuo, M., Liu, L.: Multiple positive solutions for a system of impulsive integral boundary value problems with sign-changing nonlinearities. Appl. Math. Lett. 82, 24–31 (2018)

Wu, J., Zhang, X., Liu, L., Wu, Y.: Positive solutions of higher-order nonlinear fractional differential equations with changing-sign measure. Adv. Differ. Equ. 2012, 71 (2012)

Liu, L., Hao, X., Wu, Y.: Positive solutions for singular second order differential equations with integral boundary conditions. Math. Comput. Model. 57, 836–847 (2013)

Hao, X., Liu, L.: Mild solution of semilinear impulsive integro-differential evolution equation in Banach spaces. Math. Methods Appl. Sci. 40(13), 4832–4841 (2017)

Jiang, J., Liu, L., Wu, Y.: Symmetric positive solutions to singular system with multi-point coupled boundary conditions. Appl. Math. Comput. 220, 536–548 (2013)

Hao, X., Wang, H., Liu, L., Cui, Y.: Positive solutions for a system of nonlinear fractional nonlocal boundary value problems with parameters and p-Laplacian operator. Bound. Value Probl. 2017, 182 (2017)

Zuo, M., Hao, X., Liu, L., Cui, Y.: Existence results for impulsive fractional integro-differential equation of mixed type with constant coefficient and antiperiodic boundary conditions. Bound. Value Probl. 2017, 161 (2017)

He, J., Zhang, X., Liu, L., Wu, Y.: Existence and nonexistence of radial solutions of the Dirichlet problem for a class of general k-Hessian equations. Nonlinear Anal., Model. Control 23(4), 475–492 (2018)

Xu, Y., Zhang, H.: Positive solutions of an infinite boundary value problem for nth-order nonlinear impulsive singular integro-differential equations in Banach spaces. Appl. Math. Comput. 218, 5806–5818 (2012)

Zhang, X., Shao, Z., Zhong, Q., Zhao, Z.: Triple positive solutions for semipositone fractional differential equations m-point boundary value problems with singularities and p-q-order derivatives. Nonlinear Anal., Model. Control 23(4), 889–903 (2018)

Zhang, X., Jiang, J., Wu, Y., Cui, Y.: Existence and asymptotic properties of solutions for a nonlinear Schrödinger elliptic equation from geophysical fluid flows. Appl. Math. Lett. (2018). https://doi.org/10.1016/j.aml.2018.11.011

Jiang, J., Liu, W., Wang, H.: Positive solutions to singular Dirichlet-type boundary value problems of nonlinear fractional differential equations. Adv. Differ. Equ. 2018, 169 (2018)

Hao, X., Hao, H., Liu, L.: Existence results for fractional integral boundary value problem involving fractional derivatives on an infinite interval. Math. Methods Appl. Sci. 41(16), 6984–6996 (2018)

Zhang, X., Liu, L., Wu, Y.: The entire large solutions for a quasilinear Schrödinger elliptic equation by the dual approach. Appl. Math. Lett. 55, 1–9 (2016)

Liu, J., Zhao, Z.: Multiple solutions for impulsive problems with non-autonomous perturbations. Appl. Math. Lett. 64, 143–149 (2017)

Liu, J., Zhao, Z.: An application of variational methods to second-order impulsive differential equation with derivative dependence. Electron. J. Differ. Equ. 2014, 62 (2014)

He, X., Qian, A., Zou, W.: Existence and concentration of positive solutions for quasi-linear Schrödinger equations with critical growth. Nonlinearity 26, 3137–3168 (2013)

Mao, A., Jing, R., Luan, S., Chu, J., Kong, Y.: Some nonlocal elliptic problem involving positive parameter. Topol. Methods Nonlinear Anal. 42, 207–220 (2013)

Qian, A.: Infinitely many sign-changing solutions for a Schrödinger equation. Adv. Differ. Equ. 2011, 39 (2011)

Mao, A., Zhu, X.: Existence and multiplicity results for Kirchhoff problems. Mediterr. J. Math. 14(2), 58 (2017)

Zhang, J., Lou, Z., Ji, Y., Shao, W.: Ground state of Kirchhoff type fractional Schrodinger equations with critical growth. J. Math. Anal. Appl. 462, 57–83 (2018)

Shao, M., Mao, A.: Multiplicity of solutions to Schrödinger–Poisson system with concave-convex nonlinearities. Appl. Math. Lett. 83, 212–218 (2018)

Sun, F., Liu, L., Wu, Y.: Finite time blow-up for a class of parabolic or pseudo-parabolic equations. Comput. Math. Appl. 75, 3685–3701 (2018)

Sun, F., Liu, L., Wu, Y.: Finite time blow-up for a thin-film equation with initial data at arbitrary energy level. J. Math. Anal. Appl. 458, 9–20 (2018)

Zhang, J., Lou, Z., Ji, Y., Shao, W.: Multiplicity of solutions of the bi-harmonic Schrödinger equation with critical growth. Z. Angew. Math. Phys. 69, 42 (2018)

Liu, J., Qian, A.: Ground state solution for a Schrödinger–Poisson equation with critical growth. Nonlinear Anal., Real World Appl. 40, 428–443 (2018)

Cui, Y., Zou, Y.: An existence and uniqueness theorem for a second order nonlinear system with coupled integral boundary value conditions. Appl. Math. Comput. 256, 438–444 (2015)

Wu, J., Zhang, X., Liu, L., Wu, Y.: Positive solution of singular fractional differential system with nonlocal boundary conditions. Adv. Differ. Equ. 2014, 323 (2014)