  In this article we study inverse source problems for time-fractional
diffusion equations from \textit{a posteriori} boundary measurement. Using the
memory effect of these class of equations, we solve these inverse problems for
several class of space or time dependent source terms. We prove also the unique
determination of a general class of space-time dependent separated variables
source terms from such measurement. Our approach is based on the study of
singularities of the Laplace transform in time of boundary traces of solutions
of time-fractional diffusion equations.

Analysis of PDEs