Inverse source problem with a posteriori boundary measurement for fractional diffusion equations

In this article we study inverse source problems for time-fractional diffusion equations from $\mathit{\text{a}}\mathit{\text{posteriori}}$ 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.