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Identifying a space-dependent source term in distributed order time-fractional diffusion equations

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  • The aim of this paper is to investigate an inverse problem of recovering a space-dependent source term governed by distributed order time-fractional diffusion equations in Hilbert scales. Such a problem is ill-posed and has important practical applications. For this problem, we propose a general regularization method based on the idea of the filter method. With a suitable source condition, we prove that the method is of optimal order under various choices of regularization parameter. One is based on the a priori regularization parameter choice rule and another one is the discrepancy principle. Finally, the capabilities of our method are illustrated by both the Tikhonov and the Landweber method.

    Mathematics Subject Classification: Primary: 26A33, 35R30, 47A52; Secondary: 65N15.


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