A scalable framework for solving fractional diffusion equations

A Crank-Nicolson ADI quadratic spline collocation method for two-dimensional Riemann-Liouville space-fractional diffusion equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2020.10.015 ◽

2021 ◽

Vol 160 ◽

pp. 331-348

Author(s):

Jun Liu ◽

Chen Zhu ◽

Yanping Chen ◽

Hongfei Fu

Keyword(s):

Collocation Method ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Two Dimensional ◽

Spline Collocation ◽

Quadratic Spline ◽

Spline Collocation Method ◽

Fractional Diffusion Equations ◽

Liouville Space ◽

Quadratic Spline Collocation

An implicit difference scheme for time-fractional diffusion equations with a time-invariant type variable order

Applied Mathematics Letters ◽

10.1016/j.aml.2021.107270 ◽

2021 ◽

pp. 107270

Author(s):

Xian-Ming Gu ◽

Hai-Wei Sun ◽

Yong-Liang Zhao ◽

Xiangcheng Zheng

Keyword(s):

Difference Scheme ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Variable Order ◽

Implicit Difference Scheme ◽

Fractional Diffusion Equations ◽

Type Variable ◽

Time Invariant

An efficient multigrid solver for two-dimensional spatial fractional diffusion equations with variable coefficients

Applied Mathematics and Computation ◽

10.1016/j.amc.2021.126091 ◽

2021 ◽

Vol 402 ◽

pp. 126091

Author(s):

Kejia Pan ◽

Hai-Wei Sun ◽

Yuan Xu ◽

Yufeng Xu

Keyword(s):

Fractional Diffusion ◽

Variable Coefficients ◽

Diffusion Equations ◽

Two Dimensional ◽

Multigrid Solver ◽

Fractional Diffusion Equations

Circulant-based approximate inverse preconditioners for a class of fractional diffusion equations

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2021.01.007 ◽

2021 ◽

Vol 85 ◽

pp. 18-29

Author(s):

Hong-Kui Pang ◽

Hai-Hua Qin ◽

Hai-Wei Sun ◽

Ting-Ting Ma

Keyword(s):

Fractional Diffusion ◽

Diffusion Equations ◽

Approximate Inverse ◽

Fractional Diffusion Equations

Fast algorithms for high-dimensional variable-order space-time fractional diffusion equations

Computational and Applied Mathematics ◽

10.1007/s40314-021-01496-5 ◽

2021 ◽

Vol 40 (4) ◽

Author(s):

Lei Zhang ◽

Guo-Feng Zhang

Keyword(s):

Fast Algorithms ◽

Fractional Diffusion ◽

Space Time ◽

Diffusion Equations ◽

High Dimensional ◽

Variable Order ◽

Fractional Diffusion Equations ◽

Dimensional Variable

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

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 ◽

Time Space

Lopsided scaled HSS preconditioner for steady-state space-fractional diffusion equations

CALCOLO ◽

10.1007/s10092-021-00419-4 ◽

2021 ◽

Vol 58 (2) ◽

Author(s):

Fang Chen ◽

Tian-Yi Li ◽

Galina V. Muratova

Keyword(s):

Steady State ◽

State Space ◽

Fractional Diffusion ◽

Diffusion Equations ◽

Fractional Diffusion Equations

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 ◽

Time Space

Fractional Diffusion Equations for Lattice and Continuum: Grünwald-Letnikov Differences and Derivatives Approach

International Journal of Statistical Mechanics ◽

10.1155/2014/873529 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7 ◽

Cited By ~ 3

Author(s):

Vasily E. Tarasov

Keyword(s):

Fractional Derivatives ◽

Three Dimensional ◽

Lattice Models ◽

Fractional Diffusion ◽

Lattice Diffusion ◽

Diffusion Equations ◽

Difference Operators ◽

Fractional Diffusion Equations ◽

Nonlocal Media ◽

Derivatives Of

Fractional diffusion equations for three-dimensional lattice models based on fractional-order differences of the Grünwald-Letnikov type are suggested. These lattice fractional diffusion equations contain difference operators that describe long-range jumps from one lattice site to another. In continuum limit, the suggested lattice diffusion equations with noninteger order differences give the diffusion equations with the Grünwald-Letnikov fractional derivatives for continuum. We propose a consistent derivation of the fractional diffusion equation with the fractional derivatives of Grünwald-Letnikov type. The suggested lattice diffusion equations can be considered as a new microstructural basis of space-fractional diffusion in nonlocal media.