Distributed-order space-time fractional diffusions in bounded domains

TL;DR

This paper derives explicit solutions and stochastic representations for distributed-order space-time fractional diffusion equations in bounded domains, including cases with singular mixing measures, advancing understanding of complex anomalous diffusion processes.

Contribution

It provides explicit classical solutions and stochastic analogues for distributed-order fractional diffusions, extending results to singular mixing measures in bounded domains.

Findings

Explicit classical solutions derived

Stochastic analogues constructed

Results valid for singular mixing measures

Abstract

We provide explicit classical solutions and stochastic analogues for distributed-order space-time fractional diffusion equations on bounded domains with zero exterior boundary conditions. We also show that our results still hold when the mixing measure in the distributed-order time-derivative is singular.