Computational solutions of distributed oder reactiondiffusion systems associated with RiemannLiouville derivatives
Abstract
This article is in continuation of our earlier article [37] in which computational solution of an unified reactiondiffusion equation of distributed order associated with Caputo derivatives as the timederivative and RieszFeller derivative as space derivative is derived. In this article, we present computational solutions of distributed order fractional reactiondiffusion equations associated with RiemannLiouville derivatives of fractional orders as the timederivatives and RieszFeller fractional derivatives as the space derivatives. The method followed in deriving the solution is that of joint Laplace and Fourier transforms. The solution is derived in a closed and computational form in terms of the familiar MittagLeffler function. It provides an elegant extension of the results given earlier by Chen et al. [1], Debnath [3], Saxena et al. [36], Haubold et al. [15] and Pagnini and Mainardi [30]. The results obtained are presented in the form of two theorems. Some interesting results associated with fractional Riesz derivatives are also derived as special cases of our findings. It will be seen that in case of distributed order fractional reactiondiffusion, the solution comes in a compact and closed form in terms of a generalization of the Kampé de Fériet hypergeometric series in two variables, defined by Srivastava and Daoust [46] (also see Appendix B). The convergence of the double series occurring in the solution is also given.
 Publication:

arXiv eprints
 Pub Date:
 October 2012
 arXiv:
 arXiv:1211.0063
 Bibcode:
 2012arXiv1211.0063S
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 Mathematics  Classical Analysis and ODEs
 EPrint:
 12 pages TeX