Fundamental solution and discrete random walk model for time-space fractional diffusion equation
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.
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.
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|Item Type:||Journal Article|
|Keywords:||Fractional Diffusion Equation of Distributed Order, Explicit Finite Difference Approximation, Discrete Random Walk Model, Time-Space Factional Derivative|
|Subjects:||Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200) > Dynamical Systems in Applications (010204)|
|Divisions:||Past > QUT Faculties & Divisions > Faculty of Science and Technology|
|Deposited On:||12 Feb 2010 22:50|
|Last Modified:||01 Mar 2012 11:11|
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