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Regularization Technique for an Inverse Space-Fractional Backward Heat Conduction Problem

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Abstract

This manuscript deals with a regularization technique for a generalized space-fractional backward heat conduction problem (BHCP) which is well-known to be extremely ill-posed. The presented technique is developed based on the Meyer wavelets in retrieving the solution of the presented space-fractional BHCP. Some sharp optimal estimates of the Hölder-Logarithmic type are theoretically derived by imposing an a-priori bound assumption via the Sobolev scale. The existence, uniqueness and stability of the considered problem are rigorously investigated. The asymptotic error estimates for both linear and non-linear problems are all the same. Finally, the performance of the proposed technique is demonstrated through one- and two-dimensional prototype examples that validate our theoretical analysis. Furthermore, comparative results verify that the proposed method is more effective than the other existing methods in the literature.

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Authors and Affiliations

  1. Department of Mathematics, Sahand University of Technology, P.O. Box: 51335-1996, Tabriz, Iran

    Milad Karimi, Fridoun Moradlou & Mojtaba Hajipour

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  1. Milad Karimi
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  2. Fridoun Moradlou
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  3. Mojtaba Hajipour
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Correspondence to Fridoun Moradlou.

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Karimi, M., Moradlou, F. & Hajipour, M. Regularization Technique for an Inverse Space-Fractional Backward Heat Conduction Problem. J Sci Comput 83, 37 (2020). https://doi.org/10.1007/s10915-020-01211-2

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