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

By Shujun Shen, Vo Anh and Fawang Liu


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

Topics: 010204 Dynamical Systems in Applications, Fractional Diffusion Equation of Distributed Order, Explicit Finite Difference Approximation, Discrete Random Walk Model, Time-Space Factional Derivative
Publisher: Springer
Year: 2008
DOI identifier: 10.1007/s12190-008-0084-x
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