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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).

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Author:Zivorad Tomovski, Trifce Sandev, Ralf MetzlerORCiDGND, Johan Dubbeldam
ISSN:0378-4371 (print)
ISSN:1873-2119 (online)
Parent Title (English):Physica : europhysics journal ; A, Statistical mechanics and its applications
Place of publication:Amsterdam
Document Type:Article
Year of first Publication:2012
Year of Completion: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
First Page:2527
Last Page:2542
Funder: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