TWO REGULARIZATION METHODS FOR A CLASS OF INVERSE FRACTIONAL PSEUDO–PARABOLIC EQUATIONS WITH INVOLUTION PERTURBATION
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Date
2024
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Fractional Differential Calculus
Abstract
In this study, we provide a theoretical analysis of an inverse problem governed by a time-fractional pseudo-parabolic equation with involution. The problem is characterized as ill-posed, meaning that the solution (if it exists) does not depend continuously on the measur able data. To address the inherent instability of this problem, we introduce two regularization strategies: the first employs a modified quasi-boundary value method, and the second utilizes a variant of the quasi-reversibility technique. We present convergence results under an a priori bound assumption and propose a practical a posteriori parameter selection rule.
Description
Fractional Differential Calculus, Volume 14, Number 1 (2024), 39–59