On the solutions of fractional reaction-diffusion equations

Abstract

In this paper, we obtain the solution of a fractional reaction-diffusion equation associated with the generalized Riemann-Liouville fractional derivative as the time derivative and Riesz-Feller fractional derivative as the space-derivative. The results are derived by the application of the Laplace and Fourier transforms in compact and elegant form in terms of Mittag-Leffler function and H-function. The results obtained here are of general nature and include the results investigated earlier by many authors.

Keywords

• Fractional reaction-diffusion equation
• Mittag-Leffler function
• Generalized Riemann- Liouville fractional derivative
• Caputo derivative
• Riesz-Feller fractional derivative
• Laplace transform
• Fourier transform