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 an 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 in Hilfer et al. , and the space derivative of second order by the Riesz-Feller fractional derivative, and adding a function $\varphi (x,t)$. 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 earlier by Mainardi et al., and the result very recently given by Tomovski et al.. At the end, extensions of the derived results, associated with a finite number of Riesz-Feller space fractional derivatives, are also investigated.

15 pages, LaTex

References in corpus (5)

• The fundamental solution of the space-time fractional diffusion equation
• Fractional reaction-diffusion equations
• Solution of generalized fractional reaction-diffusion equations
• Reaction-diffusion systems and nonlinear waves
• On a Generalized Entropy Measure Leading to the Pathway Model: with a preliminary application to solar neutrino data