Fundamental solution and discrete random walk model for time-space fractional diffusion equation


Autoria(s): Shen, Shujun; Anh, Vo; Liu, Fawang
Data(s)

2008

Resumo

In this paper, we consider a time-space fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advection-dispersion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α∈(0,1], the first-order and second-order space derivatives by the Riesz fractional derivatives of orders β 1∈(0,1) and β 2∈(1,2], respectively. We derive the fundamental solution for the TSFDEDO with an initial condition (TSFDEDO-IC). The fundamental solution can be interpreted as a spatial probability density function evolving in time. We also investigate a discrete random walk model based on an explicit finite difference approximation for the TSFDEDO-IC.

Formato

application/pdf

Identificador

http://eprints.qut.edu.au/30922/

Publicador

Springer

Relação

http://eprints.qut.edu.au/30922/1/Fundamental_solution_and_discrete_random_walk_model_for_time-space_fractional_diffusion_equation.pdf

DOI:10.1007/s12190-008-0084-x

Shen, Shujun, Anh, Vo, & Liu, Fawang (2008) Fundamental solution and discrete random walk model for time-space fractional diffusion equation. Journal of Applied Mathematics and Computing, 28(1-2), pp. 147-164.

Fonte

Faculty of Science and Technology

Palavras-Chave #010204 Dynamical Systems in Applications #Fractional Diffusion Equation of Distributed Order, Explicit Finite Difference Approximation, Discrete Random Walk Model, Time-Space Factional Derivative
Tipo

Journal Article