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Generalized space-time fractional diffusion equation with composite fractional time derivative
- We investigate the solution of space-time fractional diffusion equations with a generalized Riemann-Liouville time fractional derivative and Riesz-Feller space fractional derivative. The Laplace and Fourier transform methods are applied to solve the proposed fractional diffusion equation. The results are represented by using the Mittag-Leffler functions and the Fox H-function. Special cases of the initial and boundary conditions are considered. Numerical scheme and Grunwald-Letnikov approximation are also used to solve the space-time fractional diffusion equation. The fractional moments of the fundamental solution of the considered space-time fractional diffusion equation are obtained. Many known results are special cases of those obtained in this paper. We investigate also the solution of a space-time fractional diffusion equations with a singular term of the form delta(x). t-beta/Gamma(1-beta) (beta > 0).
Author details: | Zivorad Tomovski, Trifce SandevORCiDGND, Ralf MetzlerORCiDGND, Johan Dubbeldam |
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DOI: | https://doi.org/10.1016/j.physa.2011.12.035 |
ISSN: | 0378-4371 |
ISSN: | 1873-2119 |
Title of parent work (English): | Physica : europhysics journal ; A, Statistical mechanics and its applications |
Publisher: | Elsevier |
Place of publishing: | Amsterdam |
Publication type: | Article |
Language: | English |
Year of first publication: | 2012 |
Publication year: | 2012 |
Release date: | 2017/03/26 |
Tag: | Asymptotic expansions; Composite fractional derivative; Fox H-function; Fractional diffusion equation; Fractional moments; Grunwald-Letnikov approximation; Mittag-Leffler functions; Riesz-Feller fractional derivative |
Volume: | 391 |
Issue: | 8 |
Number of pages: | 16 |
First page: | 2527 |
Last Page: | 2542 |
Funding institution: | DAAD; NWO; Academy of Finland; Ministry of Education and Science of the Republic of Macedonia |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
Peer review: | Referiert |