Further solutions of fractional reaction-diffusion equations in terms of the H-function

Abstract

This paper is a continuation of our earlier paper in which we have derived the solution of an unified fractional reaction-diffusion equation associated with the Caputo derivative as the time-derivative and the Riesz-Feller fractional derivative as the space-derivative. In this paper, we consider an unified reaction-diffusion equation with Riemann-Liouville fractional derivative as the time-derivative and Riesz-Feller derivative as the space-derivative. The solution is derived by the application of the Laplace and Fourier transforms in a compact and closed form in terms of the H-function. The results derived are of general character and include the results investigated earlier by Kilbas et al. (2006a), Saxena et al. (2006c), and Mathai et al. (2010). The main result is given in the form of a theorem. A number of interesting special cases of the theorem are also given as corollaries.