Space–time fractional diffusion on bounded domains

Space–time fractional diffusion on bounded domains

Classical , Nonlocal , and Fractional Diffusion Equations on Bounded Domains

The purpose of this paper is to compare the solutions of one-dimensional boundary value problems corresponding to classical, fractional and nonlocal diffusion on bounded domains. The latter two diffusions are viable alternatives for anomalous diffusion, when Fick’s first law is an inaccurate model. In the case of nonlocal diffusion, a generalization of Fick’s first law in terms of a nonlocal fl...

Fractional Cauchy problems on bounded domains

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 ti...

Distributed-order fractional diffusions on bounded domains

Fractional Generalized Random Fields on Bounded Domains

Using the theory of generalized random fields on fractional Sobolev spaces on bounded domains, and the concept of dual generalized random field, this paper introduces a class of random fields with fractional-order pure point spectra. The covariance factorization of an a-generalized random field having a dual is established, leading to a white-noise linearfilter representation, which reduces to ...