Work

An Inverse Time-dependent Diffusion Coefficient Problem for a Space-fractional Diffusion Equation

Year: 2025

Type: article

Abstract: Space-fractional diffusion equations have recently attracted the attention of many mathematicians from various fields due to their wide-ranging practical applications. This study explores a time-dependent diffusion coefficient in a space-fractional diffusion equation, subject to initial and Dirichlet boundary conditions, along with an overdetermined dataset of integral type, representing time-integrated observations. First, we prove the existence and uniqueness of a weak solution for the direct problem. In the next step, leveraging the overdetermined condition, we refine the solution set of the inverse problem. Finally, under specific assumptions on the available data and by applying Banach’s fixed-point theorem, we demonstrate the existence, uniqueness, and stability of the solution.

Source: Fractals

DOI: 10.1142/s0218348x25402121

Authors: SMINA DJENNADI, OMAR ABU ARQUB, MARWAN ABUKHALED, NABIL SHAWAGFEH

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

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

OpenAlex ID: W4410817107

FWCI: 8.022

Cites: 28

Cited by: 5

Related to: 10