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).
Highlights
Reaction diffusion models have found numerous applications in pattern formation in biology, chemistry, and physics, see, Murray [3] and Cross and Hohenberg [4]
A piecewise linear approach in connection with the diffusive processes has been developed by Strier .Zanette and Wio [7], which leads to the analytic results in reaction - diffusion systems of wave fronts in a bistable reaction –diffusion system with density- dependent diffusivity
We present the solutions of one-dimensional linear fractional diffusion equations defined by (2.1) and (4.1)
Summary
Reaction diffusion models have found numerous applications in pattern formation in biology, chemistry, and physics, see, Murray [3] and Cross and Hohenberg [4]. These systems show that diffusion can produce the spontaneous formation of spatio- temporal patterns. In this connection, one can refer to the works of Gorenflo ,Iskende rov and Luchko [8], Hilfer [9], Mainardi, Luchko and Pagnini [10],Mainardi ,Luchko and Pagnini [10], Mainardi, Pagnini and Saxena [11], Saichev and Zaslavasky [12],Metzler and Klafter [13], Metzler and Nonnenmacher [14] , Anh and Leonenko [15], Haubold ,Mathai and Saxena [16] and others. The present study is in continuation of our investigations reported earlier in the papers by Saxena,Mathai and Haubold [19.20.21, 22, 23 ,24]
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