Strong maximum principle for fractional diffusion equations and an application to an inverse source problem

TL;DR

This paper establishes a strong maximum principle for time-fractional diffusion equations with Caputo derivatives and applies it to prove uniqueness in an inverse source problem involving the temporal component of an inhomogeneous term.

Contribution

The paper introduces a strong maximum principle for fractional diffusion equations with Caputo derivatives, extending classical results and applying it to inverse source problems.

Findings

Established a strong maximum principle for fractional diffusion equations.

Proved uniqueness for the inverse source problem involving the temporal component.

Extended maximum principle concepts from classical to fractional diffusion equations.

Abstract

The strong maximum principle is a remarkable characterization of parabolic equations, which is expected to be partly inherited by fractional diffusion equations. Based on the corresponding weak maximum principle, in this paper we establish a strong maximum principle for time-fractional diffusion equations with Caputo derivatives, which is slightly weaker than that for the parabolic case. As a direct application, we give a uniqueness result for a related inverse source problem on the determination of the temporal component of the inhomogeneous term.