# 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.

## Abstract

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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ID Code: | 30922 |
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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 |

DOI: | 10.1007/s12190-008-0084-x |

ISSN: | 1598-5865 |

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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