| [1] |
Oldham K B, Spanier J. The Fractional Calculus. New York: Academic Press, 1974
|
| [2] |
Samko S, Kilbas A A, Marichev O. Fractional Integrals and Derivatives: Theory and Applications. Oxfordshire: Taylor & Francis, 1993
|
| [3] |
Du M, Wang Z, Hu H. Measuring memory with the order of fractional derivative. Sci Rep, 2013, 3: Article number 3431
|
| [4] |
Michele C, Mauro F. A new definition of fractional derivative without singular kernel. Progr Fract Differ Appl, 2015, 1(2): 73-85
|
| [5] |
Atangana A, Baleanu D. New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. arXiv preprint arXiv:1602.03408, 2016
|
| [6] |
Cao J, Xu C. A high order schema for the numerical solution of the fractional ordinary differential equations. J Comput Phys, 2013, 38: 154-168
|
| [7] |
Cao J, Wang Z, Xu C. A high-order scheme for fractional ordinary differential equations with the Caputo Fabrizio derivative. Communications on Applied Mathematics and Computation, 2019, 1: 1-21
doi: 10.1007/s42967-019-0010-2
|
| [8] |
Yang J, Huang J, Liang D, Tang Y. Numerical solution of fractional diffusion-wave equation based on fractional multistep method. Appl Math Model, 2014, 38(14): 3652-3661
doi: 10.1016/j.apm.2013.11.069
|
| [9] |
Sun Z, Wu X. A fully discrete difference scheme for a diffusion-wave system. Appl Numer Math, 2006, 56(2): 193-209
doi: 10.1016/j.apnum.2005.03.003
|
| [10] |
Lin Y, Xu C. Finite difference/spectral approximations for the time-fractional diffusion equation. J Comput Phys, 2007, 225(2): 1533-1552
doi: 10.1016/j.jcp.2007.02.001
|
| [11] |
Jiang S, Zhang J, Zhang Q, Zhang Z. Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations. Commun Comput Phys, 2017, 21(3): 650-678
doi: 10.4208/cicp.OA-2016-0136
|
| [12] |
Huang J, Tang Y, vazquez L. Convergence analysis of a block-by-block method for fractional differential equations. Numer Math Theor Methods Appl, 2012, 5(2): 229-241
doi: 10.4208/nmtma
|
| [13] |
Alikhanov A A. A new difference scheme for the time fractional diffusion equation. J Comput Phys, 2015, 280: 424-438
doi: 10.1016/j.jcp.2014.09.031
|
| [14] |
Baffet D, Hesthaven J. A kernel compression scheme for fractional differential equations. SIAM J Numer Anal, 2017, 55(2): 496-520
doi: 10.1137/15M1043960
|
| [15] |
Baffet D, Hesthaven J. High-order accurate adaptive kernel compression time-stepping schemes for fractional differential equaitons. J Sci Comput, 2017, 72(3): 1169-1195
doi: 10.1007/s10915-017-0393-z
|
| [16] |
Deng W H. Finite element method for the space and time fractional Fokker-Planck equation. SIAM J Numer Anal, 2008, 47(1): 204-226
doi: 10.1137/080714130
|
| [17] |
Ke R H, Ng M K, Sun H W. A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations. J Comput Phys, 2015, 303: 203-211
doi: 10.1016/j.jcp.2015.09.042
|
| [18] |
Liu F, Shen S, Anh V, Turner I. Analysis of a discrete non-Markovian random walk approximation for the time fractional diffusion equation. ANZIAM J, 2005, 46: C488-C504
|
| [19] |
McLean W. Fast summation by interval clustering for an evolution equation with memory. J Sci Comput, 2012, 34(6): A3039-A3056
|
| [20] |
Hou D, Xu C. A fractional spectral method with applications to some singular problems Adv Comput Math, 2017, 343(5): 911-944
|
| [21] |
Stynes M, O'Riordan E, Gracia J. Error analysis of a finite difference method of graded meses for a time-fractional Caputo-Fabrizio derivatives. Eur Phys J C, 2016, 76: 362
doi: 10.1140/epjc/s10052-016-4209-3
|
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