Anisotropic solutions of the time-fractional diffusion equation in multiple dimensions

Abstract

Anomalous diffusion phenomena are ubiquitous in complex media, such as biological tissues. A wide class of sub-diffusive phenomena phenomena is described by the time-fractional diffusion equation. The paper investigates the case of anisotropic fractional diffusion in the Euclidean space. The solution of the fractional sub-diffusion equation can be expressed in terms of the Wright function and its spatial derivatives, parametrized by the directional unit vector (or alternatively a normal hyperplane). Moreover, the multidimensional case could be expressed as a transformation of the one-dimensional case.