The fractional space–time radial diffusion equation in terms of the Fox's H-function

Abstract

Based on a generalization of the Hilfer–Katugampola fractional operator, recently introduced, and the Weyl fractional derivative, which are responsible to describe the memory and distance effects, respectively, we investigate the anomalous diffusion in processes in which fractional radial differential equation plays an important and fundamental rule. Similarity solutions for this fractional space–time radial equation are considered. These solutions are presented in terms of the Fox's H-function. As an application, we present and discuss a special case in fractal Hausdorff dimension