TWO REGULARIZATION METHODS FOR A CLASS OF INVERSE FRACTIONAL PSEUDO–PARABOLIC EQUATIONS WITH INVOLUTION PERTURBATION

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Benabbes F., Boussetila N., LAKHDARI A.

Fractional Differential Calculus, vol.14, no.1, pp.39-59, 2024 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.7153/fdc-2024-14-03
  • Journal Name: Fractional Differential Calculus
  • Journal Indexes: Scopus
  • Page Numbers: pp.39-59
  • Keywords: Inverse problem, involution perturbation, modified quasi-boundary-value method, pseudo-parabolic problem, quasireversibility method
  • Open Archive Collection: AVESIS Open Access Collection
  • Kocaeli University Affiliated: Yes

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 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.