An Alternative Method for Solving a Certain Class of Fractional Kinetic Equations

TL;DR

This paper introduces a straightforward method using Riemann-Liouville fractional calculus operators to solve generalized fractional kinetic equations, avoiding Laplace transforms and applicable to complex physical systems.

Contribution

It presents a new simple approach for solving fractional kinetic equations using Riemann-Liouville operators, extending previous methods to more general equations.

Findings

Solution derived without Laplace transform

Applicable to complex reaction-diffusion systems

Simplifies solving fractional kinetic equations

Abstract

An alternative method for solving the fractional kinetic equations solved earlier by Haubold and Mathai (2000) and Saxena et al. (2002, 2004a, 2004b) is recently given by Saxena and Kalla (2007). This method can also be applied in solving more general fractional kinetic equations than the ones solved by the aforesaid authors. In view of the usefulness and importance of the kinetic equation in certain physical problems governing reaction-diffusion in complex systems and anomalous diffusion, the authors present an alternative simple method for deriving the solution of the generalized forms of the fractional kinetic equations solved by the aforesaid authors and Nonnenmacher and Metzler (1995). The method depends on the use of the Riemann-Liouville fractional calculus operators. It has been shown by the application of Riemann-Liouville fractional integral operator and its interesting properties, that the solution of the given fractional kinetic equation can be obtained in a straight-forward manner. This method does not make use of the Laplace transform.