References
- Samko SG, Kilbas AA, Marichev OI, Fractional Integrals and Derivatives: Theory and Applications, Yverdon: Gordon and Breach Science Publishers, 1993.
- Podlubny I, Fractional Differential Equations, Mathematics in Science and Engineering, 198 San Diego: Academic Press, 1999.
- Razminia K, Razminia A and Baleanu D, Investigation of the fractional diffusion equation based on generalized integral quadrature technique, Appl Math Modell 39 (2015), 86C98.
- Metzler R, Klafter J, The random walk's guide to anomalous diffusion: a fractional dynamics approach, Phys Reports 339 (2000), 1-77. https://doi.org/10.1016/S0370-1573(00)00070-3
- Benson DA, Wheatcraft SW and Meerschaert MM, Application of a fractional advection-dispersion equation, Water Resour Res 36 (2000), 1403-1412. https://doi.org/10.1029/2000WR900031
- Sokolov IM, Klafter J and Blumen A, Fractional kinetics, Phys Today 55 (2002), 48-54. https://doi.org/10.1063/1.1535007
- Carreras BA, Lynch VE and Zaslavsky GM, Anomalous diffusion and exit time distribution of particle tracers in plasma turbulence model, Phys Plasmas 8 (2001), 5096-5103. https://doi.org/10.1063/1.1416180
- Kirchner JW, Feng X-H and Neal C, Fractal stream chemistry and its implications for contaminant transport in catchments, Nature 403 (2000), 524-527. https://doi.org/10.1038/35000537
- Kreer M, Kizilersu A and Thomas AW, Fractional Poisson processes and their representation by infinite systems of ordinary differential equations, Stat Probab Lett. 84 (2014), 27-32. https://doi.org/10.1016/j.spl.2013.09.028
- Raberto M, Scalas E and Mainardi F, Waiting-times and returns in high-frequency financial data: an empirical study, Phys A: Stat. Mech. Appl. 314 (2002), 749-755. https://doi.org/10.1016/S0378-4371(02)01048-8
- Sabatelli L, Keating S, Dudley J and Richmond P, Waiting time distributions in financial markets, The Eur Phys J B. Condens Matter Phys. 27 (2002), 273-275.
- I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
- M.M. Meerschaert, C. Tadjeran, Finite difference approximations for two-sided space-fractional partial differential equations, Appl. Numer. Math. 56 (2006), 80-90. https://doi.org/10.1016/j.apnum.2005.02.008
- Wang H, Wang K-X and Sircar T, A direct (Nlog2N) finite difference method for fractional diffusion equations, J. Comput Phys. 229 (2010), 8095-8104. https://doi.org/10.1016/j.jcp.2010.07.011
- K.-X. Wang, H. Wang, A fast characteristic finite difference method for fractional advection-diffusion equations, Advances in Water Resources 34 (2011), 810-816. https://doi.org/10.1016/j.advwatres.2010.11.003
- F. Liu, P. Zhuang and K. Burrage, Numerical methods and analysis for a class of fractional advection-dispersion models, Comput. Math. Appl. 39 (2012), 2990-3007.
- Lin F-R, Yang S-W and Jin X-Q, Preconditioned iterative methods for fractional diffusion equation, J. Comput Phys. 256 (2014), 109-117. https://doi.org/10.1016/j.jcp.2013.07.040
- Bai Z-Z, Respectively scaled HSS iteration methods for solving discretized spatial fractional diffusion equations, J. Numer Linear Algebra With Appl. 39 (2018), e2157. https://doi.org/10.1002/nla.2157
- Chan RH, Jin X-Q, An Introduction to Iterative Toeplitz Solvers. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM), 2007.
- Golub GH, Van Loan CF, Matrix Computations, Third Edition Baltimore:The Johns Hopkins University Press, 1996.
- Y. Saad, Iterative Methods for Sparse Linear Systems, Second Edition, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2003.
- Wathen AJ, Preconditioning, Acta Numer. 24 (2015), 329-376. https://doi.org/10.1017/S0962492915000021
- P. Duhamel, M. Vetterli, Fast Fourier transforms: A tutorial review and a state of the art, Signal Processing 19 (1990), 259-299. https://doi.org/10.1016/0165-1684(90)90158-U
- Bai Z, Lu K and Pan J, Diagonal and Toeplitz splitting iteration methods for diagonal-plus-Toeplitz linear systems from spatial fractional diffusion equations, J. Numerical Linear Algebra with Applications 39 (2017), e2093.
- YuHong Ran, JunGang Wang, An ADI-like iteration method for fractional diffusion equations, J. Linear Algebra & Its Applications 39 (2016), 544-555.
- Ping-Fei Dai, Qing-Biao Wu and Sheng-Feng Zhu, Quasi-Toeplitz splitting iteration methods for unsteady space-fractional diffusion equations, J. Numer Methods Partial Differential Eq. (2018), 1-17.
- Ming-Li and Guo-Feng Zhang, Incomplete circulant and skew-circulant splitting iteration method for time-dependent space fractional diffusion equations, Japan J. Indust. Appl. Math. 33 (2016), 251-268. https://doi.org/10.1007/s13160-015-0207-3
- Sheng-Feng Wang, Ting-Zhu Huang and Xian-Ming Gu, Fast permutation preconditioning for fractional diffusion equations, J. SpringerPlus 5 (2016), 1109. https://doi.org/10.1186/s40064-016-2766-4
- R. Chan, M. Ng, Toeplitz Preconditioners for Hermitian Toeplitz Systems, J. Linear Algebra Appls. 190 (1993), 181-208. https://doi.org/10.1016/0024-3795(93)90226-E
- Michael K. Ng, Circulant and skew-circulant splitting methods for Toeplitz systems, J. Journal of Computational and Applied Mathematics 159 (2003), 101-108. https://doi.org/10.1016/S0377-0427(03)00562-4
- N. Akhondi, F. Toutounian, Accelerated Circulant and Skew Circulant Splitting Methods for Hermitian Positive Definite Toeplitz Systems, J. Advances in Numerical Analysis 10 (2012), 1151-1170.
- ZhongYun Liu, XiaoRong Qin and NianCi Wu. The shifted classical circulant and skew-circulant splitting iteration methods for Toeplitz matrix, J. Canadian mathematical bulletin 60 (2016), 1-10.
- Meerschaert MM, Tadjeran C, Finite difference approximations for two-sided space fractional partial differential equations, Appl Numer Math. 56 (2006), 80-90. https://doi.org/10.1016/j.apnum.2005.02.008
- Varga RS, Matrix Iterative Analysis, Englewood Cliffs, New Jersey: Prentice.Hall, 1962.
- Bai ZZ, Golub GH and Ng MK, Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems, J. Linear Algebra & Its Applications 428 (2003), 413-440.