Recovering Source Function and Kernel for a Time-fractional Diffusion Equation in the Bounded Domain

This article studies a inverse problem for diffusion equation on the rectangular domain. First we introduce a definition of a classical solution, and then the original problem investigate to use successive approximation. Second, the given problem is reduced to an equivalent problem. Existence and uniqueness of the solution of the equivalent problem is proved using a contraction mapping principle. Finally, using the equivalency, the existence and uniqueness of classical solution is obtained.