A Nonlinear Fractional Problem with a Second Kind Integral Condition for Time-Fractional Partial Differential Equation

Abdelwahb, Benbrahime; Oussaeif, Taki-Eddine; Ouannas, Adel; Saad, Khaled M.; Jahanshahi, Hadi; Ahmed, Diar; Aljuaid, Awad M.; Aly, Ayman A.

doi:10.1155/2022/2913587

Cited by 3 publications

(1 citation statement)

References 23 publications

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“…Mathematical modeling is a method that represents and explains a lot of real phenomena using proper mathematical formulas and approaches [1][2][3][4][5]. It can be described by a set of ordinary, partial and fractional differential equations [6][7][8][9][10]. In 1795, Gauss and Legendre elaborated the method of least square, which is the most popular parameter identification technique in mathematical modelling.…”

Section: Introductionmentioning

confidence: 99%

On sentinel method of one-phase Stefan problem

Lamya,

Batiha,

Rezzoug

et al. 2023

J. Nig. Soc. Phys. Sci.

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This paper is interested in studying the one-phase Stefan problem. For this purpose, we use the nonlinear sentinel method, which relies typically on the approximate controllability and the Fanchel-Rockafellar duality of the minimization problem, to prove the existence and uniqueness of a solution to this problem. In particular, our research focuses on the application of the nonlinear sentinel method to the single-phase Stefan problem. This approach aids in identifying an unspecified boundary section within the domain undergoing a liquid-solid phase transition. We track the evolution of the temperature profile in the liquid-solid material and the corresponding movement of its interface over time. Eventually, the local convergence used for the iterative numerical scheme is demonstrated.

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Section: Introductionmentioning

confidence: 99%

On sentinel method of one-phase Stefan problem

Lamya,

Batiha,

Rezzoug

et al. 2023

J. Nig. Soc. Phys. Sci.

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Inverse coefficient super-linear problem for a time fractional parabolic equation under integral overdetermination conditions

Benguesmia,

Oussaeif,

Rezzoug

2023

MathMon

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In this paper, we investigate the inverse problem of the determining the right-hand side of a nonlinear fractional parabolic equation with integral overdetermination condition. For the solvability of the direct problem we use the energy inequality method also known as the methode of functional analysis or the method of a priori estimates, this method has a higher character in that the existence theorem can be derived from the solution of the problem posed, begining with the uniqueness theorem. The most difficult aspect of this method is selecting the functional spaces E and F and for the unique solvability of the iverse problem is estblished under suitable conditions. The fixed point theoremis used to establish the existence and uniqueness of the solution to the inverse problem based on the data, this inverse problem appears frequently in engineering and physics modeling of various phenomena. Sismology, medicine, continuous casting, fusion welding, oil and gas production during drilling and well operation.

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Existence and uniqueness results for a semilinear fuzzy fractional elliptic equation

El,

Talhaoui,

Elomari

et al. 2023

Filomat

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The purpose of this study is to look at a family of starting value problem for semilinear fuzzy fractional elliptic equation with fractional Caputo derivatives. Firstly, we are going to extend the definition of laplacian operator under generalized H-differentiability in the Fuzzy systems. Secondly, the fuzzy integral equation are founded. Then, the existence and uniqueness of a fuzzy solution are etablished utilizing the Banach fixed point assessment method under Lipschitz conditions. Finally, we conclude our work by a conclusion.

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A Nonlinear Fractional Problem with a Second Kind Integral Condition for Time-Fractional Partial Differential Equation

Cited by 3 publications

References 23 publications

On sentinel method of one-phase Stefan problem

On sentinel method of one-phase Stefan problem

Inverse coefficient super-linear problem for a time fractional parabolic equation under integral overdetermination conditions

Existence and uniqueness results for a semilinear fuzzy fractional elliptic equation

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