Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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TWO REGULARIZATION METHODS FOR IDENTIFYING THE INITIAL VALUE OF A TIME-FRACTIONAL DIFFUSION EQUATION WITH BESSEL OPERATOR

  • G. BOUTARA (Applied Mathematics and Modelling Laboratory, Constantine 1-Brothers Mentouri University) ;
  • K. BESSILA (Applied Mathematics and Modelling Laboratory, Constantine 1, Brothers Mentouri University) ;
  • I.M. BATIHA (Department of Mathematics, Al Zaytoonah University of Jordan, Nonlinear Dynamics Research Center (NDRC), Ajman University) ;
  • D. AL-SHARO (Department of Applied Science, Ajloun College, Al-Balqa Applied University) ;
  • T.E. OUSSAEIF (Dynamic Systems and Control Laboratory, Oum El Bouaghi University) ;
  • N. ANAKIRA (Faculty of Education and Arts, Sohar University)
  • Received : 2025.12.26
  • Accepted : 2026.04.03
  • Published : 2026.05.30
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Abstract

In this work, we provide a theoretical analysis of an inverse problem governed by a time-fractional diffusion equation on a spherically symmetric domain. The problem is characterised as ill-posed. To address the instability of this problem, we employ two regularisation strategies: the first is spectral truncation, and the second is a modified quasi-boundary value regularisation method. The analysis shows that the proposed regularization schemes provide stable and reliable approximations to the unknown initial data, with a priori assumptions imposed only in the modified quasi-boundary value method. These results contribute to the theoretical development of regularization techniques for time-fractional inverse diffusion problems and may serve as a foundation for further extensions to more general inverse models.

Keywords

Acknowledgement

We acknowledge and thank the reviewers for their thorough discussion and comments.

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