Distributed-order fractional diffusions on bounded domains

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Abstract

Fractional derivatives can be used to model time delays in a diffusion process. When the order of the fractional derivative is distributed over the unit interval, it is useful for modeling a mixture of delay sources. This paper provides explicit strong solutions and stochastic analogues for distributed-order time-fractional diffusion equations on bounded domains, with Dirichlet boundary conditions.

Keywords

Fractional diffusion
Distributed-order fractional derivative
Stochastic solution
Boundary value problem

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The research of M.M.M. was partially supported by NSF grants DMS-0125486, DMS-0803360, EAR-0823965 and NIH grant R01-EB012079-01.