Fundamental solution and discrete random walk model for timespace fractional diffusion equation
Shen, Shujun, Anh, Vo, & Liu, Fawang (2008) Fundamental solution and discrete random walk model for timespace fractional diffusion equation. Journal of Applied Mathematics and Computing, 28(12), pp. 147164.

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Abstract
In this paper, we consider a timespace fractional diffusion equation of distributed order (TSFDEDO). The TSFDEDO is obtained from the standard advectiondispersion equation by replacing the firstorder time derivative by the Caputo fractional derivative of order α∈(0,1], the firstorder and secondorder 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 (TSFDEDOIC). 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 TSFDEDOIC.
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ID Code:  30922 

Item Type:  Journal Article 
Refereed:  Yes 
Keywords:  Fractional Diffusion Equation of Distributed Order, Explicit Finite Difference Approximation, Discrete Random Walk Model, TimeSpace Factional Derivative 
DOI:  10.1007/s121900080084x 
ISSN:  15985865 
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 12:50 
Last Modified:  01 Mar 2012 01:11 
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