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

Year: 2026

Type: article

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.

Source: OICC Press Journals

DOI: 10.57647/mathsci.2025.1903.14

Authors: Djennadi, Smina, Arqub, Omar Abu, Abukhaled, Marwan

Institutions: University of Béjaïa, Al-Balqa Applied University, American University of Sharjah

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7124265398

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