Well posedness for a singular two dimensional fractional initial boundary value problem with Bessel operator involving boundary integral conditions

Mesloub, Saïd; Aldosari, Faten

doi:10.3934/math.2021569

Cited by 5 publications

(5 citation statements)

References 27 publications

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“…The estimate in (54) shows that the operator G is one-to-one and that G −1 is continuous from R(G ) onto B. Consequently, if a strong solution to Problems ( 6), ( 8) and ( 9) exists, it is unique and depends continuously on the input data ϕ, ψ, f , g and the external forces F and G. Furthermore, as a consequence of ( 54), the set R(G ) ⊂ E is closed and R(G ) = R(G).…”

Section: Now Sincementioning

confidence: 99%

“…This paper can be considered a contribution to the development of traditional functional analysis methods used to prove the wellposedness of mixed problems with integral boundary conditions. For some classical cases, the reader can refer to [37,[49][50][51][52], and for some fractional cases, to [48,[53][54][55][56][57][58][59][60][61][62]. We should also mention here that there are some important papers dealing with the numerical aspects for Timoshenko systems, with many applications, for which the reader can refer to [63][64][65][66].…”

Section: Introductionmentioning

confidence: 99%

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A Non-Local Non-Homogeneous Fractional Timoshenko System with Frictional and Viscoelastic Damping Terms

Mesloub

Alhazzani

Eltayeb

2023

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We are devoted to the study of a non-local non-homogeneous time fractional Timoshenko system with frictional and viscoelastic damping terms. We are concerned with the well-posedness of the given problem. The approach relies on some functional analysis tools, operator theory, a priori estimates and density arguments. This work can be considered as a contribution to the development of energy inequality methods, the so-called a priori estimate method inspired from functional analyses and used to prove the well-posedness of mixed problems with integral boundary conditions.

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Section: Now Sincementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Non-Local Non-Homogeneous Fractional Timoshenko System with Frictional and Viscoelastic Damping Terms

Mesloub

Alhazzani

Eltayeb

2023

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“…Last but not least, the paper [28] studies similarity solutions of fractional parabolic problems with uncertainty, deriving existence results using Schauder's fixed point theorem. Finally, for the farctinoal case were σ ∈ (1,2] in (1), the reader can refer to [29].…”

Section: Introductionmentioning

confidence: 99%

On the Solvability of a Singular Time Fractional Parabolic Equation with Non Classical Boundary Conditions

Alhazzani,

Mesloub,

Gadain

2024

Fractal Fract

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This paper deals with a singular two dimensional initial boundary value problem for a Caputo time fractional parabolic equation supplemented by Neumann and non-local boundary conditions. The well posedness of the posed problem is demonstrated in a fractional weighted Sobolev space. The used method based on some functional analysis tools has been successfully showed its efficiency in proving the existence, uniqueness and continuous dependence of the solution upon the given data of the considered problem. More precisely, for proving the uniqueness of the solution of the posed problem, we established an energy inequality for the solution from which we deduce the uniqueness. For the existence, we proved that the range of the operator generated by the considered problem is dense.

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“…The presence of the integral condition creates great difficulties while performing different integrations and calculations, particularly for the fractional cases as in our problem. For fractional boundary initial value problems with nonlocal conditions, the reader can refer to [37][38][39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

On a Singular Non local Fractional System Describing a Generalized Timoshenko System with Two Frictional Damping Terms

Mesloub

Alhefthi

2023

Fractal Fract

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This paper concerns a nonhomogeneous singular fractional order system, with two frictional damping terms. This system can be considered as a generalization of the so-called Timoshenko system. Results on the existence, uniqueness, and continuous dependence on the solution were obtained via an energy approach, which mainly relies on a priori bounds and density arguments. The approach relies on functional analysis tools and operator theory. Very few results concerning the well-posedness of fractional order Timoshenko systems can be found in the literature. Our results generalize and improve the previous ones and significantly boost the development of the used method.

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Well posedness for a singular two dimensional fractional initial boundary value problem with Bessel operator involving boundary integral conditions

Cited by 5 publications

References 27 publications

A Non-Local Non-Homogeneous Fractional Timoshenko System with Frictional and Viscoelastic Damping Terms

A Non-Local Non-Homogeneous Fractional Timoshenko System with Frictional and Viscoelastic Damping Terms

On the Solvability of a Singular Time Fractional Parabolic Equation with Non Classical Boundary Conditions

On a Singular Non local Fractional System Describing a Generalized Timoshenko System with Two Frictional Damping Terms

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