Space-time fractional Dirichlet problems

Boris Baeumer; Tomasz Luks; Mark M. Meerschaert

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arXiv · 1604.06421

Space-time fractional Dirichlet problems

Boris Baeumer·Tomasz Luks·Mark M. Meerschaert

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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.

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BibTeX RIS

Boris Baeumer, Tomasz Luks, Mark M. Meerschaert. 2016-04-19. Space-time fractional Dirichlet problems. https://arxiv.org/abs/1604.06421

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