  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.
