Solutions For A Generalized Fractional Anomalous Diffusion Equation

TL;DR

This paper derives explicit solutions for a generalized fractional diffusion equation with spatially and temporally varying coefficients and external forces, linking these solutions to maximum entropy principles.

Contribution

It introduces a new analytical approach to solving a generalized fractional diffusion equation with variable coefficients and external forces, connecting solutions to Tsallis entropy.

Findings

Explicit analytical solutions for the generalized fractional diffusion equation.

Relation established between solutions and Tsallis entropy-based maximum entropy principle.

Enhanced understanding of anomalous diffusion processes with external forces.

Abstract

In this paper, we investigate the solutions for a generalized fractional diffusion equation that extends some known diffusion equations by taking a spatial time-dependent diffusion coefficient and an external force into account, which subjects to the natural boundaries and the generic initial condition. We obtain explicit analytical expressions for the probability distribution and study the relation between our solutions and those obtained within the maximum entropy principle by using the Tsallis entropy.