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Stochastic solution of space-time fractional diffusion equations.

Authors
  • Meerschaert, Mark M
  • Benson, David A
  • Scheffler, Hans-Peter
  • Baeumer, Boris
Type
Published Article
Journal
Physical Review E
Publisher
American Physical Society (APS)
Publication Date
Apr 01, 2002
Volume
65
Issue
4 Pt 1
Pages
41103–41103
Identifiers
PMID: 12005802
Source
Medline
License
Unknown

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.

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