Distributed order reaction-diffusion systems associated with Caputo derivatives
| Autor: | Saxena, R. K., Mathai, A. M., Haubold, H. J. |
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| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | J. Math. Phys. 55 (2014) 083519 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1063/1.4891922 |
| Popis: | This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation of distributed order associated with the Caputo derivatives as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the joint Laplace and Fourier transforms in compact and closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by other authors, notably by Mainardi et al. [23,24], for the fundamental solution of the space-time fractional equation, including Haubold et al. [13] and Saxena et al. [38] for fractional reaction-diffusion equations. The advantage of using the Riesz-Feller derivative lies in the fact that the solution of the fractional reaction-diffusion equation, containing this derivative, includes the fundamental solution for space-time fractional diffusion, which itself is a generalization of fractional diffusion, space-time fraction diffusion, and time-fractional diffusion. These specialized types of diffusion can be interpreted as spatial probability density functions evolving in time and are expressible in terms of the H-function in compact forms. The convergence conditions for the double series occurring in the solutions are investigated. It is interesting to observe that the double series comes out to be a special case of the Srivastava-Daoust hypergeometric function of two variables given in the Appendix B of this paper. Comment: 13 pages, Plain TeX |
| Databáze: | arXiv |
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