Solutions of time fractional anomalous diffusion equations with coefficients depending on both time and space variables

TL;DR

This paper derives explicit solutions for time-fractional anomalous diffusion equations with space- and time-dependent coefficients, using Fox-H and generalized Wright functions, advancing understanding in this complex area.

Contribution

It introduces explicit solutions for a class of anomalous diffusion equations with variable coefficients, expressed through special functions.

Findings

Explicit solutions derived using Fox-H functions

Solutions applicable to various fields involving anomalous diffusion

Enhanced understanding of diffusion with variable coefficients

Abstract

We derive explicit solutions for time-fractional anomalous diffusion equations with diffusivity coefficients that depend on both space and time variables. These solutions are expressed in Fox-H and generalized Wright functions, which are commonly used in anomalous diffusion equations. Our study represents a significant advancement in our understanding of anomalous diffusion with potential applications in a wide range of fields.