Stochastic solution of space-time fractional diffusion equations

Mark M. Meerschaert, David A. Benson, Hans-Peter Scheffler, and Boris Baeumer
Phys. Rev. E 65, 041103 – Published 28 March 2002
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Abstract

Classical and anomalous diffusion equations employ integer derivatives, fractional derivatives, and other pseudodifferential operators in space. In this paper we show that replacing the integer time derivative by a fractional derivative subordinates the original stochastic solution to an inverse stable subordinator process whose probability distributions are Mittag-Leffler type. This leads to explicit solutions for space-time fractional diffusion equations with multiscaling space-fractional derivatives, and additional insight into the meaning of these equations.

  • Received 16 July 2001

DOI:https://doi.org/10.1103/PhysRevE.65.041103

©2002 American Physical Society

Authors & Affiliations

Mark M. Meerschaert*

  • Department of Mathematics, University of Nevada, Reno, Nevada 89557-0084

David A. Benson

  • Desert Research Institute, 2215 Raggio Parkway, Reno, Nevada 89506-0220

Hans-Peter Scheffler

  • Fachbereich Mathematik, University of Dortmund, 44221 Dortmund, Germany

Boris Baeumer

  • Department of Mathematics and Statistics, University of Otago, Dunedin, New Zealand

  • *Electronic address: mcubed@unr.edu

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Vol. 65, Iss. 4 — April 2002

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