A posteriori regularization parameter choice rule for a modified kernel method for a time-fractional inverse diffusion problem

Abstract In this paper, we consider a time-fractional inverse diffusion problem (TFIDP), where the measured data is given at x = 1 and the solution is required in the interval 0 ≤ x 1 . We show that TFIDP is severely ill-posed and further apply a modified kernel method to deal with this problem based on the solution in the frequency domain. The convergence estimate is obtained by using a posteriori parameter choice rule. Numerical examples show that the proposed method works effectively.