  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.
