Similarity Solution for Fractional Diffusion Equation

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 $p(r,t)$, which is just the fundamental solution of the fractional diffusion equation, was expressed in terms of Fox functions.