DETERMINATION OF THE SOURCE TERM IN AN INVERSE FRACTIONAL PARABOLIC PROBLEM WITH A TIME-DEPENDENT COEFFICIENT

Iqbal M. Batiha; Aida Azzi; Mohammad S. Hijazi; Taki Eddine Oussaeif; Nidal Anakira; Fatma Achab; Imad Rezzoug

doi:10.54379/jiasf-2026-1-1

DETERMINATION OF THE SOURCE TERM IN AN INVERSE FRACTIONAL PARABOLIC PROBLEM WITH A TIME-DEPENDENT COEFFICIENT

Iqbal M. Batiha
, Aida Azzi
, Mohammad S. Hijazi
, Taki Eddine Oussaeif
, Nidal Anakira
, Fatma Achab
, Imad Rezzoug

Nonlinear Dynamic Research Centre (NDRC)

Al-Zaytoonah University of Jordan
University of Oum El Bouaghi
Al Jouf University
Sohar University

Research output: Contribution to journal › Article › peer-review

Abstract

In this article, we study an inverse fractional problem that is ill-posed in the sense of Hadamard. The goal is to recover a source term in a time-fractional parabolic equation with a time-dependent coefficient, using Tikhonov regularization. A no-regret control approach is employed to address the regularization problem when the initial condition is unknown. The source term is characterized through the corresponding optimality system.

Original language	English
Pages (from-to)	1-17
Number of pages	17
Journal	Journal of Inequalities and Special Functions
Volume	17
Issue number	1
DOIs	https://doi.org/10.54379/jiasf-2026-1-1
State	Published - 2026

Keywords

Inverse fractional problem
Tikhonov regularization
optimality system
source term identification

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10.54379/jiasf-2026-1-1

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title = "DETERMINATION OF THE SOURCE TERM IN AN INVERSE FRACTIONAL PARABOLIC PROBLEM WITH A TIME-DEPENDENT COEFFICIENT",

abstract = "In this article, we study an inverse fractional problem that is ill-posed in the sense of Hadamard. The goal is to recover a source term in a time-fractional parabolic equation with a time-dependent coefficient, using Tikhonov regularization. A no-regret control approach is employed to address the regularization problem when the initial condition is unknown. The source term is characterized through the corresponding optimality system.",

keywords = "Inverse fractional problem, Tikhonov regularization, optimality system, source term identification",

author = "Batiha, \{Iqbal M.\} and Aida Azzi and Hijazi, \{Mohammad S.\} and Oussaeif, \{Taki Eddine\} and Nidal Anakira and Fatma Achab and Imad Rezzoug",

note = "Publisher Copyright: {\textcopyright}2026 Ilirias Research Institute, Prishtin{\"e}, Kosov{\"e}.",

year = "2026",

doi = "10.54379/jiasf-2026-1-1",

language = "English",

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T1 - DETERMINATION OF THE SOURCE TERM IN AN INVERSE FRACTIONAL PARABOLIC PROBLEM WITH A TIME-DEPENDENT COEFFICIENT

AU - Batiha, Iqbal M.

AU - Azzi, Aida

AU - Hijazi, Mohammad S.

AU - Oussaeif, Taki Eddine

AU - Anakira, Nidal

AU - Achab, Fatma

AU - Rezzoug, Imad

PY - 2026

Y1 - 2026

N2 - In this article, we study an inverse fractional problem that is ill-posed in the sense of Hadamard. The goal is to recover a source term in a time-fractional parabolic equation with a time-dependent coefficient, using Tikhonov regularization. A no-regret control approach is employed to address the regularization problem when the initial condition is unknown. The source term is characterized through the corresponding optimality system.

AB - In this article, we study an inverse fractional problem that is ill-posed in the sense of Hadamard. The goal is to recover a source term in a time-fractional parabolic equation with a time-dependent coefficient, using Tikhonov regularization. A no-regret control approach is employed to address the regularization problem when the initial condition is unknown. The source term is characterized through the corresponding optimality system.

KW - Inverse fractional problem

KW - Tikhonov regularization

KW - optimality system

KW - source term identification

UR - https://www.scopus.com/pages/publications/105034597415

U2 - 10.54379/jiasf-2026-1-1

DO - 10.54379/jiasf-2026-1-1

M3 - Article

AN - SCOPUS:105034597415

SN - 2217-4303

VL - 17

SP - 1

EP - 17

JO - Journal of Inequalities and Special Functions

JF - Journal of Inequalities and Special Functions

IS - 1

ER -

DETERMINATION OF THE SOURCE TERM IN AN INVERSE FRACTIONAL PARABOLIC PROBLEM WITH A TIME-DEPENDENT COEFFICIENT

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Keywords

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