Space‐time fractional Dirichlet problems

Boris Baeumer, Tomasz Luks and Mark M. Meerschaert

Mathematische Nachrichten, 2018, vol. 291, issue 17-18, 2516-2535

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.

Date: 2018
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