Strong positivity property and a related inverse source problem for multi-term time-fractional diffusion equations

TL;DR

This paper establishes positivity properties for multi-term time-fractional diffusion equations, proves uniqueness in an inverse source problem, and demonstrates the effectiveness of the proposed numerical algorithm.

Contribution

It introduces a positivity result for solutions, proves uniqueness for a related inverse problem, and provides numerical validation for the method.

Findings

Solution positivity when source is nonpositive

Uniqueness of inverse source determination

Numerical experiments confirm accuracy and efficiency

Abstract

In this article, we consider the diffusion equation with multi-term time-fractional derivatives. We first derive that the solution is positive when the source term is nonpositive by a subordination principle for the solution. As an application, we prove that the uniqueness of the inverse problem on the determination of the temporally varying source term by integral type information in a subdomain. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.