Unified Fractional Kinetic Equation and a Fractional Diffusion Equation

Details Unified Fractional Kinetic Equation and a Fractional Diffusion Equation Unified Fractional Kinetic Equation and a Fractional Diffusion Equation

2004-06-22

arxiv.org/abs/math-ph/0406047v1

Astrophysics and Space Science 290(2004)299-310

Physics

Mathematical Physics

13 pages, LaTeX

Scientific paper

10.1023/B:ASTR.0000032531.46639.

In earlier papers Saxena et al. (2002, 2003) derived the solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which extended the work of Haubold and Mathai (2000). The object of the present paper is to investigate the solution of a unified form of fractional kinetic equation in which the free term contains any integrable function f(t), which provides the unification and extension of the results given earlier recently by Saxena et al. (2002, 2003). The solution has been developed in terms of the Wright function in a closed form by the method of Laplace transform. Further we derive a closed-form solution of a fractional diffusion equation. The asymptotic expansion of the derived solution with respect to the space variable is also discussed. The results obtained are in a form suitable for numerical computation.

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