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Space‐time fractional Dirichlet problems

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  • Boris Baeumer
  • Tomasz Luks
  • Mark M. Meerschaert

Abstract

This paper establishes explicit solutions for fractional diffusion problems on bounded domains. It also gives stochastic solutions, in terms of Markov processes time‐changed by an inverse stable subordinator whose index equals the order of the fractional time derivative. Some applications are given, to demonstrate how to specify a well‐posed Dirichlet problem for space‐time fractional diffusions in one or several variables. This solves an open problem in numerical analysis.

Suggested Citation

  • Boris Baeumer & Tomasz Luks & Mark M. Meerschaert, 2018. "Space‐time fractional Dirichlet problems," Mathematische Nachrichten, Wiley Blackwell, vol. 291(17-18), pages 2516-2535, December.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:17-18:p:2516-2535
    DOI: 10.1002/mana.201700111
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