Space-time fractional reaction-diffusion equations associated with a generalized riemann-liouville fractional derivative

Abstract

This paper deals with the investigation of the computational solutions of a unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized Riemann-Liouville fractional derivative defined by others and the space derivative of second order by the Riesz-Feller fractional derivative and adding a function ϕ(x; t). The solution is derived by the application of the Laplace and Fourier transforms in a compact and closed form in terms of Mittag-Leffler functions. The main result obtained in this paper provides an elegant extension of the fundamental solution for the space-time fractional diffusion equation obtained by others and the result very recently given by others. At the end, extensions of the derived results, associated with a finite number of Riesz-Feller space fractional derivatives, are also investigated.