Mekoth, C.George, S.Padikkal, J.Erappa, S.M.2026-02-042022Partial Differential Equations in Applied Mathematics, 2022, 5, , pp. -https://doi.org/10.1016/j.padiff.2021.100246https://idr.nitk.ac.in/handle/123456789/22557One of the intuitive restrictions of infinite dimensional Fractional Tikhonov Regularization Method (FTRM) for ill-posed operator equations is its numerical realization. This paper addresses the issue to a considerable extent by using its finite dimensional realization in the setting of Hilbert scales. Using adaptive parameter choice strategy, we choose the regularization parameter and obtain an optimal order error estimate. Also, the proposed method is applied to the well known examples in the setting of Hilbert scales. © 2021 The Author(s)Adaptive parameter choice strategyFinite dimensional Fractional Tikhonov regularizationHilbert scalesIll-posed problem