Strong Maximum Principle for Multi-Term Time-Fractional Diffusion Equations and its Application to an Inverse Source Problem

Abstract

In this paper, we establish a strong maximum principle for fractional diffusion equations with multiple Caputo derivatives in time, and investigate a related inverse problem of practical importance. Exploiting the solution properties and the involved multinomial Mittag-Leffler functions, we improve the weak maximum principle for the multi-term time-fractional diffusion equation to a stronger one, which is parallel to that for its single-term counterpart as expected. As a direct application, we prove the uniqueness for determining the temporal component of the source term with the help of the fractional Duhamel's principle for the multi-term case.

17 pages

References in corpus (2)

• A Tutorial on Inverse Problems for Anomalous Diffusion Processes
• Strong maximum principle for fractional diffusion equations and an application to an inverse source problem

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