Solutions for a fractional diffusion equation in heterogeneous media

Abstract

We investigate diffusive phenomena governed by fractional diffusion equations in the presence of a spatial dependent diffusion coefficient and external forces. We consider a fractional operator which enables us to analyze, in a unified way, different types of fractional time derivatives. This approach opens the possibility of considering new situations related to memory effects. After determining exact analytical solutions, we show that different diffusive behaviors can be obtained, depending on the fractional time operator employed. In this framework, we also discuss the role of the anomalous diffusion processes.