Identification of the Source Term of an Ill-Posed Inverse Fractional Parabolic Problem

Fatma Achab; Iqbal M. Batiha; Taki Eddine Oussaeif; Imad Rezzoug

doi:10.5269/bspm.79523

Identification of the Source Term of an Ill-Posed Inverse Fractional Parabolic Problem

Fatma Achab
, Iqbal M. Batiha
, Taki Eddine Oussaeif
, Imad Rezzoug

Nonlinear Dynamic Research Centre (NDRC)

University of Oum El Bouaghi
Al-Zaytoonah University of Jordan

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

Abstract

In this paper, we investigate an ill-posed inverse fractional problem in the sense of Hadamard. Our objective is to identify the source term using Tikhonov regularization. Since the initial condition is missing, the no-regret control approach is employed to solve the regularization problem. The source term is characterized through an associated optimality system.

Original language	English
Journal	Boletim da Sociedade Paranaense de Matematica
Volume	43
Issue number	2
DOIs	https://doi.org/10.5269/bspm.79523
State	Published - 13 Aug 2025

Keywords

35R30
47A52
49K05
93B30
Inverse fractional problem
Tikhonov regularization
identification of the source term
optimality system

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10.5269/bspm.79523

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abstract = "In this paper, we investigate an ill-posed inverse fractional problem in the sense of Hadamard. Our objective is to identify the source term using Tikhonov regularization. Since the initial condition is missing, the no-regret control approach is employed to solve the regularization problem. The source term is characterized through an associated optimality system.",

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author = "Fatma Achab and Batiha, \{Iqbal M.\} and Oussaeif, \{Taki Eddine\} and Imad Rezzoug",

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AU - Batiha, Iqbal M.

AU - Oussaeif, Taki Eddine

AU - Rezzoug, Imad

N1 - Publisher Copyright: © Soc. Paran. de Mat.

PY - 2025/8/13

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N2 - In this paper, we investigate an ill-posed inverse fractional problem in the sense of Hadamard. Our objective is to identify the source term using Tikhonov regularization. Since the initial condition is missing, the no-regret control approach is employed to solve the regularization problem. The source term is characterized through an associated optimality system.

AB - In this paper, we investigate an ill-posed inverse fractional problem in the sense of Hadamard. Our objective is to identify the source term using Tikhonov regularization. Since the initial condition is missing, the no-regret control approach is employed to solve the regularization problem. The source term is characterized through an associated optimality system.

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KW - 47A52

KW - 49K05

KW - 93B30

KW - Inverse fractional problem

KW - Tikhonov regularization

KW - identification of the source term

KW - optimality system

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JF - Boletim da Sociedade Paranaense de Matematica

IS - 2

ER -

Identification of the Source Term of an Ill-Posed Inverse Fractional Parabolic Problem

Abstract

Keywords

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