From the space-time fractional integral of the continuous time random walk to the space-time fractional diffusion equations, a short proof and simulation

DOI10.1016/j.physa.2019.121547OpenAlexW2946091255MaRDI QIDQ2162536

Entsar A. Abdel-Rehim

Publication date: 8 August 2022

Published in: Physica A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physa.2019.121547

zbMATH Keywords

Mittag-Leffler functionintegral equationFokker-Planck equationstochastic processescontinuous time random walkdiffusion processessimulation by Monte Carlo methodspace-time fractional derivatives

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Fractional derivatives and integrals (26A33) Wave equation (35L05) Diffusion processes (60J60) Other functions defined by series and integrals (33E20) Finite difference methods for boundary value problems involving PDEs (65N06) Stable stochastic processes (60G52) Pseudodifferential operators (47G30) Statistical mechanics, structure of matter (82-XX)

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Cites Work

• Fundamental solutions of the fractional diffusion and the fractional Fokker-Planck equations
• From the Ehrenfest model to time-fractional stochastic processes
• From power laws to fractional diffusion: the direct way
• Continuous-time random walk and parametric subordination in fractional diffusion
• Simulation of the continuous time random walk of the space-fractional diffusion equations
• Relaxation patterns and semi-Markov dynamics
• Asymptotics for conservation laws involving Lévy diffusion generators
• Random Walks on Lattices. II
• Fractional diffusion and wave equations
• The fundamental solution of the space-time fractional diffusion equation
• Random walk models approximating symmetric space-fractional diffusion processes
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