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, cilt.14, sa.1, ss.39-59, 2024 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.7153/fdc-2024-14-03
  • Dergi Adı: Fractional Differential Calculus
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.39-59
  • Anahtar Kelimeler: Inverse problem, involution perturbation, modified quasi-boundary-value method, pseudo-parabolic problem, quasireversibility method
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Kocaeli Üniversitesi Adresli: Evet

Özet

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.