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Abstract and Applied Analysis
Volume 2014, Article ID 548126, 5 pages
http://dx.doi.org/10.1155/2014/548126
Research Article

Similarity Solution for Fractional Diffusion Equation

1School of Sciences, Shanghai Institute of Technology, Shanghai 201418, China
2School of Mathematics, Baotou Teachers College, Baotou, Inner Mongolia 014030, China

Received 4 January 2014; Accepted 11 February 2014; Published 12 March 2014

Academic Editor: Ming Li

Copyright © 2014 Jun-Sheng Duan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Fractional diffusion equation in fractal media is an integropartial differential equation parametrized by fractal Hausdorff dimension and anomalous diffusion exponent. In this paper, the similarity solution of the fractional diffusion equation was considered. Through the invariants of the group of scaling transformations we derived the integro-ordinary differential equation for the similarity variable. Then by virtue of Mellin transform, the probability density function , which is just the fundamental solution of the fractional diffusion equation, was expressed in terms of Fox functions.