Transient anomalous sub-diffusion on bounded domains

TL;DR

This paper develops analytical and stochastic methods to solve the tempered fractional diffusion equation on bounded domains, including eigenvalue problems, eigenfunction expansions, and inverse subordinator representations.

Contribution

It introduces new solutions for the tempered fractional diffusion equation on bounded domains, combining eigenfunction expansions and stochastic representations.

Findings

Eigenvalue problem for tempered fractional derivatives solved

Strong solutions via separation of variables derived

Stochastic solutions expressed through inverse subordinator

Abstract

This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables, and eigenfunction expansions in time and space, are used to write strong solutions. Finally, stochastic solutions are written in terms of an inverse subordinator.