No abstract

In this paper, we consider a time-fractional inverse diffusion problem, where the data is given at x = 1 and the solution is sought in the interval 0 ≤ x < 1. Such a problem is obtained from the classical diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative of order α ∈ (0, 1). We show that a time-fractional inverse diffusion problem is severely ill-posed and we further apply a modified kernel method to solve it based on the solution in the frequency domain. The corresponding convergence estimates are provided. Finally, an example is constructed to show the feasibility and efficiency of the proposed method. MSC: 35R25; 35R30; 47A52