Solutions of the Fractional Reaction Equation and the Fractional Diffusion Equation

TL;DR

This paper derives explicit solutions for fractional reaction and diffusion equations using Fox and Mittag-Leffler functions, extending previous results and providing a unified approach for these types of equations.

Contribution

The authors present a unified explicit solution for a general fractional reaction equation and introduce a shorter method for solving fractional diffusion equations.

Findings

Explicit solutions expressed in Fox and Mittag-Leffler functions

Extension and unification of earlier fractional reaction equation results

Simplified method for fractional diffusion equation solutions

Abstract

In view of the role of reaction equations in physical problems, the authors derive the explicit solution of a fractional reaction equation of general character, that unifies and extends earlier results. Further, an alternative shorter method based on a result developed by the authors is given to derive the solution of a fractional diffusion equation. Fox functions and Mittag-Leffler functions are used for closed-form representations of the solutions of the respective differential equations.