The modified fractional-order quasi-reversibility method for a class of direct and inverse problems governed by time-fractional heat equations with involution perturbation

Benabbes F., Boussetila N., Lakhdari A.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.47, no.12, pp.9524-9555, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 12
  • Publication Date: 2024
  • Doi Number: 10.1002/mma.10081
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.9524-9555
  • Kocaeli University Affiliated: No

Abstract

This study aims to explore two classes of ill-posed problems governed by a nonclassical fractional heat equation with an involution perturbation. To achieve a stable solution, we introduce a modified pseudo-parabolic regularization method that involves a correction term through a mixed fractional derivation operator, resulting in a sequence of well-posed problems that depend on a regularization parameter epsilon$$ \varepsilon $$. We rigorously demonstrate that the resulting approximate problems are well-posed and present convergence results for this regularization approach.