Optimal error bound and truncation regularization method for a backward time-fractional diffusion problem in Hilbert scales

Abstract In this paper, we investigate a backward problem for a time-fractional diffusion equation in a general abstract Hilbert space. We show that the problem is ill-posed and further apply a truncation regularization method to solve it. Based on a Holder-type smoothness assumption of the exact solution, asymptotically optimal estimates for the worst case error of the method in Hilbert scales are proved.

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