Fast implicit difference schemes for time‐space fractional diffusion equations with the integral fractional Laplacian

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.6746 ◽

2020 ◽

Vol 44 (1) ◽

pp. 441-463

Author(s):

Xian‐Ming Gu ◽

Hai‐Wei Sun ◽

Yanzhi Zhang ◽

Yong‐Liang Zhao

Keyword(s):

Fractional Laplacian ◽

Fractional Diffusion ◽

Difference Schemes ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

Implicit Difference Schemes

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Two Alternating Direction Implicit Difference Schemes for Two-Dimensional Distributed-Order Fractional Diffusion Equations

Journal of Scientific Computing ◽

10.1007/s10915-015-0064-x ◽

2015 ◽

Vol 66 (3) ◽

pp. 1281-1312 ◽

Author(s):

Guang-hua Gao ◽

Zhi-zhong Sun

Keyword(s):

Fractional Diffusion ◽

Difference Schemes ◽

Diffusion Equations ◽

Two Dimensional ◽

Alternating Direction Implicit ◽

Fractional Diffusion Equations ◽

Alternating Direction ◽

Implicit Difference Schemes ◽

Distributed Order

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Finite difference schemes for the two-dimensional multi-term time-fractional diffusion equations with variable coefficients

Computational and Applied Mathematics ◽

10.1007/s40314-021-01551-1 ◽

2021 ◽

Vol 40 (5) ◽

Author(s):

Mingrong Cui

Keyword(s):

Finite Difference ◽

Fractional Diffusion ◽

Variable Coefficients ◽

Difference Schemes ◽

Diffusion Equations ◽

Finite Difference Schemes ◽

Two Dimensional ◽

Fractional Diffusion Equations

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A fractional Tikhonov regularization method for an inverse backward and source problems in the time-space fractional diffusion equations

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2021.111127 ◽

2021 ◽

Vol 150 ◽

pp. 111127

Author(s):

Smina Djennadi ◽

Nabil Shawagfeh ◽

Omar Abu Arqub

Keyword(s):

Tikhonov Regularization ◽

Regularization Method ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Tikhonov Regularization Method ◽

Fractional Diffusion Equations ◽

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Backward problem for time-space fractional diffusion equations in Hilbert scales

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2021.04.018 ◽

2021 ◽

Vol 93 ◽

pp. 253-264

Author(s):

Dang Duc Trong ◽

Dinh Nguyen Duy Hai

Keyword(s):

Fractional Diffusion ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

Backward Problem ◽

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A unified difference-spectral method for time–space fractional diffusion equations

International Journal of Computer Mathematics ◽

10.1080/00207160.2016.1184262 ◽

2016 ◽

Vol 94 (6) ◽

pp. 1172-1184 ◽

Author(s):

Jianfei Huang ◽

Dandan Yang

Keyword(s):

Spectral Method ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

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Invariant subspaces and exact solutions for some types of scalar and coupled time-space fractional diffusion equations

Pramana ◽

10.1007/s12043-020-01964-3 ◽

2020 ◽

Vol 94 (1) ◽

Author(s):

P Prakash

Keyword(s):

Exact Solutions ◽

Invariant Subspaces ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

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Crank-Nicolson-weighted-shifted-Grünwald-difference schemes for space Riesz variable-order fractional diffusion equations

Numerical Algorithms ◽

10.1007/s11075-020-00980-z ◽

2020 ◽

Author(s):

Fu-Rong Lin ◽

Qiu-Ya Wang ◽

Xiao-Qing Jin

Keyword(s):

Fractional Diffusion ◽

Difference Schemes ◽

Diffusion Equations ◽

Variable Order ◽

Fractional Diffusion Equations ◽

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Efficient second-order ADI difference schemes for three-dimensional Riesz space-fractional diffusion equations

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2021.06.016 ◽

2021 ◽

Vol 98 ◽

pp. 24-39

Author(s):

Chen Zhu ◽

Bingyin Zhang ◽

Hongfei Fu ◽

Jun Liu

Keyword(s):

Three Dimensional ◽

Fractional Diffusion ◽

Second Order ◽

Riesz Space ◽

Difference Schemes ◽

Diffusion Equations ◽

Fractional Diffusion Equations

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Finite difference method for time–space linear and nonlinear fractional diffusion equations

International Journal of Computer Mathematics ◽

10.1080/00207160.2017.1344231 ◽

2017 ◽

Vol 95 (1) ◽

pp. 202-217 ◽

Author(s):

Sadia Arshad ◽

Weiping Bu ◽

Jianfei Huang ◽

Yifa Tang ◽

Yue Zhao

Keyword(s):

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Fractional Diffusion Equations ◽

Linear And Nonlinear

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Maximum norm error analysis of difference schemes for fractional diffusion equations

Applied Mathematics and Computation ◽

10.1016/j.amc.2014.12.151 ◽

2015 ◽

Vol 256 ◽

pp. 299-314 ◽

Author(s):

Jincheng Ren ◽

Zhi-zhong Sun

Keyword(s):

Error Analysis ◽

Fractional Diffusion ◽

Difference Schemes ◽

Diffusion Equations ◽

Maximum Norm ◽

Fractional Diffusion Equations ◽

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