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In this paper, we establish a strong maximum principle for fractionaldiffusion equations with multiple Caputo derivatives in time, and investigate arelated inverse problem of practical importance. Exploiting the solutionproperties and the involved multinomial Mittag-Leffler functions, we improvethe weak maximum principle for the multi-term time-fractional diffusionequation to a stronger one, which is parallel to that for its single-termcounterpart as expected. As a direct application, we prove the uniqueness fordetermining the temporal component of the source term with the help of thefractional Duhamel's principle for the multi-term case.

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