1 |
Singh C S , Singh H , Singh V K , Singh Om P . Fractional order operational matrix methods for fractional singular integro-differential equation. Appl Math Model, 2016, 40, 10705- 10718
doi: 10.1016/j.apm.2016.08.011
|
2 |
Rehman M U , Khan R A . A numerical method for solving boundary value problems for fractional differential equations. Appl Math Model, 2012, 36, 894- 907
doi: 10.1016/j.apm.2011.07.045
|
3 |
Zahra W K , Van Daele M . Discrete spline methods for solving two point fractional Bagley-Torvik equation. Appl Math Comput, 2017, 296, 42- 56
|
4 |
Pedas A , Tamme E , Vikerpuur M . Smoothing transformation and spline collocation for nonlinear fractional initial and boundary value problems. J Comput Appl Math, 2017, 317, 1- 16
doi: 10.1016/j.cam.2016.11.022
|
5 |
Karraslan M F , Celiker F , Kurulay M . Approximate solution of the Bagley-Torvik equation by hybridizable discontinuous Galerkin methods. Appl Math Comput, 2016, 285, 51- 58
|
6 |
El-Ajou A , Aequb O A , Momani S . Solving fractional two-point boundary value problems using continuous analytic method. Ain Shams Eng J, 2013, 4, 539- 547
doi: 10.1016/j.asej.2012.11.010
|
7 |
Hashim I , Abdulaziz O , Momani S . Homotopy analysis method for fractional IVPs. Commun Nonlinear Sci Numer Simul, 2009, 14, 674- 684
doi: 10.1016/j.cnsns.2007.09.014
|
8 |
Daftardar-Gejji V , Jafari H . Solving a multi-order fractional differential equation using adomian decomposition. Appl Math Comput, 2007, 189, 541- 548
|
9 |
Abdulaziz O, Hashim I, Momani S. Solving systems of fractional differential equations by homotopy-perturbation method. Phys Lett, 2008, A372:451-459
|
10 |
Wu G, Lee E W M. Fractional variational iteration method and its application. Phys Lett, 2010, A374:2506-2509
|
11 |
Odibat Z , Momani S , Suat Erturk V . Generalized differential transform method:application to differential equations of fractional order. Appl Math Comput, 2008, 197, 467- 477
|
12 |
Arikoglu A , Ozkol I . Solution of fractional differential equations by using differential transform method. Chaos Soliton Frac, 2007, 34, 1473- 1481
doi: 10.1016/j.chaos.2006.09.004
|
13 |
Reutskiy S Yu . A novel method for solving second order fractional eigenvalue problems. J Comput Appl Math, 2016, 306, 133- 153
doi: 10.1016/j.cam.2016.04.003
|
14 |
Zhang Y . A finite difference method for fractional partial differential equation. Appl Math Comput, 2009, 215, 524- 529
|
15 |
Daftardar-Gejji V , Jhinga A . A new finite-difference predictor-corrector method for fractional differential equations. Appl Math Comput, 2018, 336, 418- 432
|
16 |
Baleanu D , Shiri B . Collocation methods for fractional differential equations involving non-singular kernel. Chaos Soliton Frac, 2018, 116, 136- 145
doi: 10.1016/j.chaos.2018.09.020
|
17 |
Ziane D , Baleanu D , Belghaba K , Hamdi Cherif M . Local fractional Sumudu decomposition method for linear partial differential equations with local fractional derivative. Journal of King Saud University-Science, 2019, 31, 83- 88
doi: 10.1016/j.jksus.2017.05.002
|
18 |
Zhou Y T , Zhang C J . Convergence and stability of block boundary value methods applied to nonlinear fractional differential equations with Caputo derivatives. Appl Numer Math, 2019, 135, 367- 380
doi: 10.1016/j.apnum.2018.09.010
|
19 |
Mohammadi F , Cattani C . A generalized fractional-order Legendre wavelet Tau method for solving fractional differential equations. J Comput Appl Math, 2018, 339, 306- 316
doi: 10.1016/j.cam.2017.09.031
|
20 |
Bakhtiari P , Abbasbanda S , Van Gorder R A . Reproducing kernel method for the numerical solution of the 1D Swift-Hohenberg equation. Appl Math Comput, 2018, 339, 132- 143
|
21 |
Niu J , Xu M Q , Yao G M . An efficient reproducing kernel method for solving the Allen-Cahn equation. Appl Math Lett, 2019, 89, 78- 84
doi: 10.1016/j.aml.2018.09.013
|
22 |
Mei L C , Lin Y Z . Simplified reproducing kernel method and convergence order for linear Volterra integral equations with variable coefficients. J Comput Appl Math, 2019, 346, 390- 398
doi: 10.1016/j.cam.2018.07.027
|
23 |
Li X Y , Wu B Y . A numerical technique for variable fractional functional boundary value problems. Appl Math Lett, 2015, 43, 108- 113
doi: 10.1016/j.aml.2014.12.012
|
24 |
Yang J B , Yao H M , Wu B Y . An efficient numerical method for variable order fractional functional differential equation. Appl Math Lett, 2018, 76, 221- 226
doi: 10.1016/j.aml.2017.08.020
|
25 |
Geng F Z , Cui M G . A reproducing kernel method for solving nonlocal fractional boundary value problem. Appl Math Lett, 2012, 25, 818- 823
doi: 10.1016/j.aml.2011.10.025
|
26 |
Li X Y , Wu B Y . A new reproducing kernel method for variable order fractional boundary value problems for functional differential equations. J Comput Appl Math, 2017, 311, 387- 393
doi: 10.1016/j.cam.2016.08.010
|
27 |
Xu M Q , Lin Y Z . Simplified reproducing kernel method for fractional differential equations with delay. Appl Math Lett, 2016, 52, 156- 161
doi: 10.1016/j.aml.2015.09.004
|
28 |
Li X Y , Li H , Wu B Y . A new numerical method for variable order fractional functional differential equations. Appl Math Lett, 2017, 68, 80- 86
doi: 10.1016/j.aml.2017.01.001
|
29 |
张禾瑞, 郝鈵新. 高等代数(第五版). 北京: 高等教育出版社, 2007
|
|
Zhang H R , Hao B X . Advanced Algebra (Fifth Edition). Beijing: Higher Education Press, 2007
|
30 |
吴勃英, 林迎珍. 应用型再生核空间. 北京: 科学出版社, 2012
|
|
Wu B Y , Lin Y Z . Application of the Reproducing Kernel Space. Beijing: Science Press, 2012
|