Solution of a modified fractional diffusion equation

Langlands, T. A. M. (2006) Solution of a modified fractional diffusion equation. Physica A: Statistical Mechanics and Its Applications, 367. pp. 136-144. ISSN 0378-4371

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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.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Deposited in accordance with the copyright policy of the publisher.
Depositing User: Dr Trevor Langlands
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 30 Oct 2009 08:59
Last Modified: 02 Jul 2013 23:20
Uncontrolled Keywords: modified fractional diffusion equation, anomalous diffusion, Fox function
Fields of Research (FOR2008): 01 Mathematical Sciences > 0101 Pure Mathematics > 010110 Partial Differential Equations
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: doi: 10.1016/j.physa.2005.12.012
URI: http://eprints.usq.edu.au/id/eprint/5436

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