Distributed-order fractional Cauchy problems on bounded domains

Details Distributed-order fractional Cauchy problems on bounded domains Distributed-order fractional Cauchy problems on bounded domains

2009-12-13

arxiv.org/abs/0912.2521v1

Journal of Mathematical Analysis and Applications 379 (2011) 216-228

Mathematics

Probability

29 pages

Scientific paper

10.1016/j.jmaa.2010.12.056

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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