Unified Fractional Kinetic Equation and a Fractional Diffusion Equation

TL;DR

This paper develops a unified fractional kinetic equation incorporating a general free term and derives its solution using Wright functions, also providing a closed-form solution for a fractional diffusion equation with asymptotic analysis.

Contribution

It introduces a unified fractional kinetic equation with a general free term and derives its solution in closed form using Wright functions, extending previous models.

Findings

Solution expressed in terms of Wright functions

Unified framework for fractional kinetic equations

Asymptotic expansion of the solution

Abstract

In earlier papers Saxena et al. (2002, 2003) derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which extended the work of Haubold and Mathai (2000). The object of the present paper is to investigate the solution of a unified form of fractional kinetic equation in which the free term contains any integrable function f(t), which provides the unification and extension of the results given earlier recently by Saxena et al. (2002, 2003). The solution has been developed in terms of the Wright function in a closed form by the method of Laplace transform. Further we derive a closed-form solution of a fractional diffusion equation. The asymptotic expansion of the derived solution with respect to the space variable is also discussed. The results obtained are in a form suitable for numerical computation.