Fractional Cauchy problems on bounded domains
Mark M. Meerschaert, Erkan Nane, and P. Vellaisamy
Source: Ann. Probab. Volume 37, Number 3 (2009), 979-1007.
Abstract
Fractional Cauchy problems replace the usual first-order time derivative by a fractional derivative. This paper develops classical solutions and stochastic analogues for fractional Cauchy problems in a bounded domain D⊂ℝd with Dirichlet boundary conditions. Stochastic solutions are constructed via an inverse stable subordinator whose scaling index corresponds to the order of the fractional time derivative. Dirichlet problems corresponding to iterated Brownian motion in a bounded domain are then solved by establishing a correspondence with the case of a half-derivative in time.
Primary Subjects: 60G99, 35C10
Keywords: Fractional diffusion; Cauchy problem; iterated Brownian motion; Brownian subordinator; Caputo derivative; uniformly elliptic operator; bounded domain; boundary value problem
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aop/1245434026
Digital Object Identifier: doi:10.1214/08-AOP426
Zentralblatt MATH identifier:
05587821
Mathematical Reviews number (MathSciNet):
MR2537547
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