Solution of One –dimensional Fractional Diffusion Equations Involving Caputo Fractional Derivatives in terms of the Mittag - Leffler Functions

摘要

The object of this article is to investigate the solutions of one-dimensional linear fractional diffusion equations defined by (2.1) and (4.1). The solutions are obtained in a closed and elegant forms in terms of the H-function and generalized Mittag - Leffler functions, which are suitable for numerical computation. The derived results include the results for the one-dimentional linear fractional telegraph equation due to Orsingher and Beghin [1], and recently derived results by Saxena ,Mathai and Haubold [2].