An inverse source problem for a two parameter anomalous diffusion equation with nonlocal boundary conditions

We consider the inverse problem of determination of the solution and a source term for a time fractional diffusion equation in two dimensional space. The time fractional derivative is the Hilfer derivative. A bi-orthogonal system of functions in L2(Ω), obtained from the associated non-self-adjoint spectral problem and its adjoint problem, is used to prove the existence and uniqueness of the solution of the inverse problem. The stability of the solution of the inverse problem on the given data is proved.