An inverse problem for a generalized fractional diffusion

We propose a method for determining the solution and source term of a generalized time-fractional diffusion equation. The method is based on selecting a bi-orthogonal basis of L2 space corresponding to a nonself-adjoint boundary value problem. Uniqueness is proven and an existence result is obtained for smooth initial and final conditions. The asymptotic behavior of the generalized Mittag-Leffler function is used to relax the smoothness requirement on these conditions.