A time-fractional Fokker-Planck initial-boundary value problem is considered with a space and time-dependent forcing. The problem is more difficult to analyze than the case of space-dependent forcing which has been investigated by other authors. In this talk, existence, uniqueness and regularity of both mild and classical solutions are studied by using Galerkin approximations and compactness arguments. Furthermore, estimates of time derivatives of the classical solution are derived—these are known to be needed in numerical analyses of this problem.