Solution of a modified fractional diffusion equation

Article

Langlands, T. A. M.. 2006. "Solution of a modified fractional diffusion equation." Physica A: Statistical Mechanics and its Applications. 367, pp. 136-144. https://doi.org/10.1016/j.physa.2005.12.012
Article Title

Solution of a modified fractional diffusion equation

ERA Journal ID351
Article CategoryArticle
Authors
AuthorLanglands, T. A. M.
Journal TitlePhysica A: Statistical Mechanics and its Applications
Journal Citation367, pp. 136-144
Number of Pages9
Year2006
Place of PublicationNetherlands
ISSN0378-4371
1873-2119
Digital Object Identifier (DOI)https://doi.org/10.1016/j.physa.2005.12.012
Web Address (URL)https://www.sciencedirect.com/science/article/pii/S0378437105012604
Abstract

Recently, a modified fractional diffusion equation has been proposed [I. Sokolov, J. Klafter, From diffusion to anomalous diffusion: a century after Einstein’s brownian motion, Chaos 15 (2005) 026103; A.V. Chechkin, R. Gorenflo, I.M. Sokolov, V.Yu. Gonchar, Distributed order time fractional diffusion equation, Frac. Calc. Appl. Anal. 6 (3) (2003) 259–279; I.M. Sokolov, A.V. Chechkin, J. Klafter, Distributed-order time fractional kinetics, Acta. Phys. Pol. B 35 (2004) 1323.] for describing processes that become less anomalous as time progresses by the inclusion of a second fractional time derivative acting on the diffusion term. In this letter we give the solution of the modified equation on an infinite domain. In contrast to the solution of the traditional fractional diffusion equation, the solution of the modified equation requires a summation of Fox functions instead of a single Fox function.

Keywordsmodified fractional diffusion equation, anomalous diffusion, Fox function
Contains Sensitive ContentDoes not contain sensitive content
ANZSRC Field of Research 2020490410. Partial differential equations
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Byline AffiliationsUniversity of New South Wales
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