Two regularization methods for a class of inverse fractional pseudo-parabolic equations with involution perturbation

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 measurable 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.

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