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arXiv · 0912.2521

Distributed-order fractional Cauchy problems on bounded domains

Mark M. Meerschaert·Erkan Nane·Palaniappan Vellaisamy
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Abstract

In a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. The fractional derivative models time delays in a diffusion process. The order of the fractional derivative can be distributed over the unit interval, to model a mixture of delay sources. In this paper, we provide explicit strong solutions and stochastic analogues for distributed-order fractional Cauchy problems on bounded domains with Dirichlet boundary conditions. Stochastic solutions are constructed using a non-Markovian time change of a killed Markov process generated by a uniformly elliptic second order space derivative operator.

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Mark M. Meerschaert, Erkan Nane, Palaniappan Vellaisamy. 2009-12-13. Distributed-order fractional Cauchy problems on bounded domains. https://doi.org/10.1016/j.jmaa.2010.12.056

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