Space-time fractional diffusion on bounded domains

TL;DR

This paper develops strong solutions and probabilistic representations for space-time fractional diffusion equations on bounded domains, aiding the modeling of anomalous diffusion in physics and improving particle tracking methods.

Contribution

It introduces new mathematical solutions and probabilistic models for fractional diffusion equations on bounded domains, enhancing understanding and computational approaches.

Findings

Established strong solutions for fractional diffusion equations.

Provided probabilistic representations for particle tracking.

Enhanced modeling of anomalous diffusion processes.

Abstract

Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional diffusion equations on bounded domains, as well as probabilistic representations of these solutions, which are useful for particle tracking codes.