محمد شهریاری

‎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.