We consider the inverse source problem of determining a source term depending
on both time and space variable for fractional and classical diffusion
equations in a cylindrical domain from boundary measurements. With suitable
boundary conditions we prove that some class of source terms which are
independent of one space direction, can be reconstructed from boundary
measurements. Actually, we prove that this inverse problem is well-posed. We
establish also some results of Lipschitz stability for the recovery of source
terms which we apply to the stable recostruction of time-dependent
coefficients
