ON FRACTIONAL BIPARABOLIC INVERSE SOURCE PROBLEM

Lakhdari A., Boussetila N., Abdeljawad T., BEN Makhlouf A.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, vol.22, pp.353-371, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22
  • Publication Date: 2026
  • Doi Number: 10.3934/dcdss.2024216
  • Journal Name: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, MathSciNet, zbMATH
  • Page Numbers: pp.353-371
  • Kocaeli University Affiliated: No

Abstract

This paper addresses a fractional biparabolic inverse source problem that integrates fractional derivatives with the biparabolic equation to achieve a more precise characterization of anomalous diffusion. We show that this problem is ill-posed according to Hadamard's sense. To tackle the instability associated with this problem, we apply regularization techniques using the Landweber iterative method. We provide convergence estimates based on a priori information on the exact solution. The paper concludes with numerical experiments that confirm the validity of the proposed theoretical framework.