An inverse problem for a generalized fractional diffusion

摘要

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.