Transient anomalous sub-diffusion on bounded domains

Meerschaert, Mark; Nane, Erkan; Vellaisamy, P.

doi:10.1090/S0002-9939-2012-11362-0

Transient anomalous sub-diffusion on bounded domains
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by Mark M. Meerschaert, Erkan Nane and P. Vellaisamy PDF

Proc. Amer. Math. Soc. 141 (2013), 699-710 Request permission

Abstract:

This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables and eigenfunction expansions in time and space are used to write strong solutions. Finally, stochastic solutions are written in terms of an inverse subordinator.

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