Heidel, Gennadij; Khoromskaia, Venera; Khoromskij, Boris N.; Schulz, Volker Tensor product method for fast solution of optimal control problems with fractional multidimensional Laplacian in constraints. (English) Zbl 07508470 J. Comput. Phys. 424, Article ID 109865, 21 p. (2021). MSC: 65-XX 15-XX PDFBibTeX XMLCite \textit{G. Heidel} et al., J. Comput. Phys. 424, Article ID 109865, 21 p. (2021; Zbl 07508470) Full Text: DOI arXiv
Zan, Wanrong; Xu, Yong; Metzler, Ralf; Kurths, Jürgen First-passage problem for stochastic differential equations with combined parametric Gaussian and Lévy white noises via path integral method. (English) Zbl 07503736 J. Comput. Phys. 435, Article ID 110264, 20 p. (2021). MSC: 60Jxx 82Cxx 60Gxx PDFBibTeX XMLCite \textit{W. Zan} et al., J. Comput. Phys. 435, Article ID 110264, 20 p. (2021; Zbl 07503736) Full Text: DOI
Lischke, Anna; Pang, Guofei; Gulian, Mamikon; Song, Fangying; Glusa, Christian; Zheng, Xiaoning; Mao, Zhiping; Cai, Wei; Meerschaert, Mark M.; Ainsworth, Mark; Karniadakis, George Em What is the fractional Laplacian? A comparative review with new results. (English) Zbl 1453.35179 J. Comput. Phys. 404, Article ID 109009, 62 p. (2020). MSC: 35R11 60G51 35A01 35A02 65N30 65C05 35-02 65-02 PDFBibTeX XMLCite \textit{A. Lischke} et al., J. Comput. Phys. 404, Article ID 109009, 62 p. (2020; Zbl 1453.35179) Full Text: DOI Link
Sales Teodoro, G.; Tenreiro Machado, J. A.; de Oliveira, E. Capelas A review of definitions of fractional derivatives and other operators. (English) Zbl 1452.26008 J. Comput. Phys. 388, 195-208 (2019). MSC: 26A33 26A24 26-02 PDFBibTeX XMLCite \textit{G. Sales Teodoro} et al., J. Comput. Phys. 388, 195--208 (2019; Zbl 1452.26008) Full Text: DOI
Rundell, William; Zhang, Zhidong Recovering an unknown source in a fractional diffusion problem. (English) Zbl 1392.35333 J. Comput. Phys. 368, 299-314 (2018). MSC: 35R30 35R11 35A02 35R05 65M32 PDFBibTeX XMLCite \textit{W. Rundell} and \textit{Z. Zhang}, J. Comput. Phys. 368, 299--314 (2018; Zbl 1392.35333) Full Text: DOI arXiv Link
Arshad, Sadia; Huang, Jianfei; Khaliq, Abdul Q. M.; Tang, Yifa Trapezoidal scheme for time-space fractional diffusion equation with Riesz derivative. (English) Zbl 1380.65141 J. Comput. Phys. 350, 1-15 (2017). MSC: 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{S. Arshad} et al., J. Comput. Phys. 350, 1--15 (2017; Zbl 1380.65141) Full Text: DOI
Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon A fast semi-discrete Kansa method to solve the two-dimensional spatiotemporal fractional diffusion equation. (English) Zbl 1380.65310 J. Comput. Phys. 345, 74-90 (2017). MSC: 65M70 35R11 PDFBibTeX XMLCite \textit{H. Sun} et al., J. Comput. Phys. 345, 74--90 (2017; Zbl 1380.65310) Full Text: DOI arXiv
Chen, Hu; Lü, Shujuan; Chen, Wenping Finite difference/spectral approximations for the distributed order time fractional reaction-diffusion equation on an unbounded domain. (English) Zbl 1349.65507 J. Comput. Phys. 315, 84-97 (2016). MSC: 65M70 65M15 35R11 35K57 PDFBibTeX XMLCite \textit{H. Chen} et al., J. Comput. Phys. 315, 84--97 (2016; Zbl 1349.65507) Full Text: DOI
Stokes, Peter W.; Philippa, Bronson; Read, Wayne; White, Ronald D. Efficient numerical solution of the time fractional diffusion equation by mapping from its Brownian counterpart. (English) Zbl 1352.65268 J. Comput. Phys. 282, 334-344 (2015). MSC: 65M06 35R11 PDFBibTeX XMLCite \textit{P. W. Stokes} et al., J. Comput. Phys. 282, 334--344 (2015; Zbl 1352.65268) Full Text: DOI arXiv
Ye, H.; Liu, Fawang; Anh, V. Compact difference scheme for distributed-order time-fractional diffusion-wave equation on bounded domains. (English) Zbl 1349.65353 J. Comput. Phys. 298, 652-660 (2015). MSC: 65M06 65M12 35R11 PDFBibTeX XMLCite \textit{H. Ye} et al., J. Comput. Phys. 298, 652--660 (2015; Zbl 1349.65353) Full Text: DOI Link
Mentrelli, Andrea; Pagnini, Gianni Front propagation in anomalous diffusive media governed by time-fractional diffusion. (English) Zbl 1349.35404 J. Comput. Phys. 293, 427-441 (2015). MSC: 35R11 35K57 60G22 60J60 PDFBibTeX XMLCite \textit{A. Mentrelli} and \textit{G. Pagnini}, J. Comput. Phys. 293, 427--441 (2015; Zbl 1349.35404) Full Text: DOI Link
Bologna, Mauro; Svenkeson, Adam; West, Bruce J.; Grigolini, Paolo Diffusion in heterogeneous media: an iterative scheme for finding approximate solutions to fractional differential equations with time-dependent coefficients. (English) Zbl 1349.82003 J. Comput. Phys. 293, 297-311 (2015). MSC: 82-08 65M99 82C80 35R11 PDFBibTeX XMLCite \textit{M. Bologna} et al., J. Comput. Phys. 293, 297--311 (2015; Zbl 1349.82003) Full Text: DOI
Bu, Weiping; Tang, Yifa; Wu, Yingchuan; Yang, Jiye Finite difference/finite element method for two-dimensional space and time fractional Bloch-Torrey equations. (English) Zbl 1349.65440 J. Comput. Phys. 293, 264-279 (2015). MSC: 65M60 65M06 35R11 65M12 PDFBibTeX XMLCite \textit{W. Bu} et al., J. Comput. Phys. 293, 264--279 (2015; Zbl 1349.65440) Full Text: DOI
Luchko, Yuri Wave-diffusion dualism of the neutral-fractional processes. (English) Zbl 1349.35402 J. Comput. Phys. 293, 40-52 (2015). MSC: 35R11 PDFBibTeX XMLCite \textit{Y. Luchko}, J. Comput. Phys. 293, 40--52 (2015; Zbl 1349.35402) Full Text: DOI
Chacón, L.; del-Castillo-Negrete, D.; Hauck, C. D. An asymptotic-preserving semi-Lagrangian algorithm for the time-dependent anisotropic heat transport equation. (English) Zbl 1349.82072 J. Comput. Phys. 272, 719-746 (2014). MSC: 82C80 65M80 82D10 PDFBibTeX XMLCite \textit{L. Chacón} et al., J. Comput. Phys. 272, 719--746 (2014; Zbl 1349.82072) Full Text: DOI
Gao, Guang-hua; Sun, Zhi-zhong; Zhang, Hong-wei A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications. (English) Zbl 1349.65088 J. Comput. Phys. 259, 33-50 (2014). MSC: 65D25 34A08 PDFBibTeX XMLCite \textit{G.-h. Gao} et al., J. Comput. Phys. 259, 33--50 (2014; Zbl 1349.65088) Full Text: DOI
Podlubny, Igor; Chechkin, Aleksei; Skovranek, Tomas; Chen, Yangquan; Vinagre Jara, Blas M. Matrix approach to discrete fractional calculus. II: Partial fractional differential equations. (English) Zbl 1160.65308 J. Comput. Phys. 228, No. 8, 3137-3153 (2009). MSC: 65D25 65M06 91B82 65Z05 PDFBibTeX XMLCite \textit{I. Podlubny} et al., J. Comput. Phys. 228, No. 8, 3137--3153 (2009; Zbl 1160.65308) Full Text: DOI arXiv
Chen, Chang-Ming; Liu, Fawang; Turner, I.; Anh, V. A Fourier method for the fractional diffusion equation describing sub-diffusion. (English) Zbl 1165.65053 J. Comput. Phys. 227, No. 2, 886-897 (2007). Reviewer: Pat Lumb (Chester) MSC: 65M12 65M70 35B35 PDFBibTeX XMLCite \textit{C.-M. Chen} et al., J. Comput. Phys. 227, No. 2, 886--897 (2007; Zbl 1165.65053) Full Text: DOI Link