The problem of determining the source term $ f=f(x) $ in a time fractional diffusion equation from the measured data at the final time is formulated. To this end, a methodology involving minimization of the cost functional is applied and proved that the Fr\'{e}chet derivative of the cost functional can be formulated via the solution of an adjoint problem. The obtained results permit one to prove existence and uniqueness of a quasi solution of the considered inverse problems, as well as to construct a monotone iteration scheme based on a gradient-type method.
