10.57647/mathsci.2025.1903.14

On Recovering a Time-dependent Inverse Problem in the Diffusion Model with a Dirichlet-type Constraint and an Integral Overposed Condition: Theory and Simulation

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  • Smina Djennadi1,
  • Omar Abu Arqub*2,
  • Marwan Abukhaled3,
  1. Department of Mathematics, Faculty of Sciences, University of Bejaia, Bejaia 06000, Algeria
  2. Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan
  3. Department of Mathematics and Statistics, American University of Sharjah, Sharjah 26666, United Arab Emirates

Received: 2025-08-25

Revised: 2025-09-22

Accepted: 2025-09-27

Published in Issue 2025-09-30

Copyright (c) 2025 Smina Djennadi, Omar Abu Arqub, Marwan Abukhaled (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Djennadi, S., Arqub, O. A., & Abukhaled, M. (2025). On Recovering a Time-dependent Inverse Problem in the Diffusion Model with a Dirichlet-type Constraint and an Integral Overposed Condition: Theory and Simulation. Mathematical Sciences, 19(3). https://doi.org/10.57647/mathsci.2025.1903.14
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Abstract

Our aim in this paper is to recover a time-dependent source term, along with the solution of the diffusion equation, by using a new definition of the derivative, known as the conformable approach. Herein, the inverse problem is utilized subject to Dirichlet boundary constraint conditions and an integral overposed condition. An explicit solution in series form for the considered inverse source problem is obtained by employing the Fourier expansion scheme. The thoughtful mathematical structure, including the theoretical (existence, stability, and uniqueness) for the suggested regular solution, is settled and affirmed. Two time-conformable diffusion equation examples are considered to show the stability result. Various graphical plots and numerical tables are utilized to confirm the results discussed. The final remarks, highlights, and some focused references are given at the end.

Keywords

  • Diffusion equation,
  • Inverse source problem,
  • Fourier expansion method,
  • Time-conformable derivative,
  • Numerical simulation
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