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FDE : Fractional Differential Equations
Survey and Review
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What is a fractional derivative?,
M. D. Ortigueira and J. A. T. Machadob, JCP, 293(2015), 4--13.
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Computational challenge of fractional differential equations and the potential solutions: A survey,
Chunye Gong, Weimin Bao, Guojian Tang, Yuewen Jiang and Jie Liu, Mathematical Problems in Engineering, 2015
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A review of definitions for fractional derivatives and integral,
E. C. de Oliveira1 and J. A. T. Machado, Mathematical Problems in Engineering, 2014
Papers
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A direct $O(N\log^2N)$ finite difference method for fractional diffusion equations,
H. Wang, K. Wang, and T. Sircar, JCP, 229 (2010), 8095--8104.
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An $O(N\log^2N)$ alternating-direction finite difference method
for two-dimensional fractional diffusion equations,
H. Wang and K. Wang, JCP, 230 (2011), 7830--7839.
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Multigrid method for fractional diffusion equations,
H. Pang and H. Sun, JCP, 231 (2012), 693--703.
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A superfast-preconditioned iterative method for steady-state space-fractional diffusion equations,
H. Wang and N. Du, JCP, 240(2013), 49--57.
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A circulant preconditioner for fractional diffusion equations,
S. L. Lei and H. W. Sun, JCP, 242(2013), 715--725.
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Wellposedness of Variable-Coefficient Conservative Fractional Elliptic Differential Equations,
H. Wang and D. P. Yang, SINUM, 51(2013), 1088--1107.
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Preconditioning techniques for diagonal-times-Toeplitz matrices in fractional diffusion equations,
M. K. Ng, J. Y. Pan and H. W. Sun, SISC, 36(2014), A2698--A2719.
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Fast approximate inversion of a block triangular Toeplitz matrix with applications to fractional sub‐diffusion equations,
X. Lu, H.‐K. Pang and H.‐W. Sun, Numer. Linear Algebra Appl., 22 (2015), 866--882.
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A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations,
R. H. Ke, M. K. Ng and H.-W. Sun, Journal of Computational Physics, 303 (2015), 203--211.
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A divide-and-conquer fast finite difference method for space–time fractional partial differential equation,
H. F. Fu, M. K. Ng and H. Wang, Computers & Mathematics with Applications, 73 (2017), 1233--1242.
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Solving mixed classical and fractional partial differential equations using short–memory principle and approximate inverses,
D. Bertaccini and F. Durastante, Numerical Algorithms, 74 (2017), 1061--1082.
Books
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分数阶偏微分方程数值方法及其应用,
刘发旺, 庄平辉, 刘青霞, 科学出版社, 2015
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分数阶微分方程的有限差分方法,
孙志忠, 高广花, 科学出版社, 2015
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Numerical Methods for Fractional Calculus,
Changpin Li (李常品) and Fanhai Zeng, CRC Press, 2015
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Basic Theory of Fractional Differential Equations,
Yong Zhou, World Scientific, 2014
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分数阶偏微分方程及其数值解,
郭柏灵, 蒲学科, 黄凤辉, 科学出版社, 2011
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力学与工程问题的分数阶导数建模,
陈文、孙洪广、李西成, 科学出版社, 2010
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Theory and Applications of Fractional Differential Equations,
A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Elsevier, 2006
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Fractional Differential Equations,
I. Podlubny, Academic Press, 1999
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Fractional Integrals and Derivatives - Theory and Applications,
S. G. Samko, A. A. Kilbas and O. I. Marichev, 1993
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