Mathematics and Statistics Vol. 2(1), pp. 15 - 26
DOI: 10.13189/ms.2014.020103
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Solution of One –dimensional Fractional Diffusion Equations Involving Caputo Fractional Derivatives in terms of the Mittag - Leffler Functions

R.K. Saxena ^*
Department of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur 342004, India

ABSTRACT

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].

KEYWORDS
Fractional Diffusion equation, Laplace transform, Fourier transform, Generalized Mittag–Leffler function, H-function, Caputo fractional derivative

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] R.K. Saxena , "Solution of One –dimensional Fractional Diffusion Equations Involving Caputo Fractional Derivatives in terms of the Mittag - Leffler Functions," Mathematics and Statistics, Vol. 2, No. 1, pp. 15 - 26, 2014. DOI: 10.13189/ms.2014.020103.

(b). APA Format:
R.K. Saxena (2014). Solution of One –dimensional Fractional Diffusion Equations Involving Caputo Fractional Derivatives in terms of the Mittag - Leffler Functions. Mathematics and Statistics, 2(1), 15 - 26. DOI: 10.13189/ms.2014.020103.