Generalized space–time fractional diffusion equation with composite fractional time derivative

Živorad Tomovski, Trifce Sandev, Ralf Metzler and Johan Dubbeldam

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 8, 2527-2542

Abstract: 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 Grünwald–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 δ(x)⋅t−βΓ(1−β)(β>0).

Keywords: Fractional diffusion equation; Composite fractional derivative; Riesz–Feller fractional derivative; Mittag-Leffler functions; Fox H-function; Fractional moments; Asymptotic expansions; Grünwald–Letnikov approximation (search for similar items in EconPapers)
Date: 2012
References: View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S037843711100971X
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:8:p:2527-2542

DOI: 10.1016/j.physa.2011.12.035

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().