Further solutions of fractional reaction–diffusion equations in terms of the -function

✍ Scribed by H.J. Haubold; A.M. Mathai; R.K. Saxena

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 215 KB
• Volume: 235
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2010.08.016

✦ Synopsis

This paper is in continuation of our earlier paper in which we have derived the solution of a unified fractional reaction-diffusion equation associated with the Caputo derivative as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. In this paper, we consider a unified reaction-diffusion equation with the Riemann-Liouville fractional derivative as the time-derivative and Riesz-Feller derivative as the space-derivative. The solution is derived by the application of the Laplace and Fourier transforms in a compact and closed form in terms of the H-function. The results derived are of general character and include the results investigated earlier in . The main result is given in the form of a theorem. A number of interesting special cases of the theorem are also given as corollaries.