Uniqueness of solutions for a<i>ψ</i>-Hilfer fractional integral boundary value problem with the<i>p</i>-Laplacian operator

Alsaedi, Ahmed; Alghanmi, Madeaha; Ahmad, Bashir; Alharbi, Boshra

doi:10.1515/dema-2022-0195

Cited by 6 publications

(3 citation statements)

References 30 publications

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“…In [39][40][41][42][43][44][45][46], there are studies on the existence of mild solutions of differential equations and inclusions involving the w -weighted Φ-Hilfer fractional derivative of order µ ∈ (0, 1) and of type v ∈ [0, 1] in the special case w(σ) = 1; ∀σ ∈ ℑ.…”

Section: Introductionmentioning

confidence: 99%

Mild Solutions for w-Weighted, Φ-Hilfer, Non-Instantaneous, Impulsive, w-Weighted, Fractional, Semilinear Differential Inclusions of Order μ ∈ (1, 2) in Banach Spaces

Alsheekhhussain,

Ibrahim,

Al-Sawalha

et al. 2024

Fractal Fract

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The aim of this work is to obtain novel and interesting results for mild solutions to a semilinear differential inclusion involving a w-weighted, Φ-Hilfer, fractional derivative of order μ∈(1,2) with non-instantaneous impulses in Banach spaces with infinite dimensions when the linear term is the infinitesimal generator of a strongly continuous cosine family and the nonlinear term is a multi-valued function. First, we determine the formula of the mild solution function for the considered semilinear differential inclusion. Then, we give sufficient conditions to ensure that the mild solution set is not empty or compact. The desired results are achieved by using the properties of both the w-weighted Φ-Laplace transform, w-weighted ψ-convolution and the measure of non-compactness. Since the operator, the w-weighted Φ-Hilfer, includes well-known types of fractional differential operators, our results generalize several recent results in the literature. Moreover, our results are novel because no one has previously studied these types of semilinear differential inclusions. Finally, we give an illustrative example that supports our theoretical results.

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Section: Introductionmentioning

confidence: 99%

Mild Solutions for w-Weighted, Φ-Hilfer, Non-Instantaneous, Impulsive, w-Weighted, Fractional, Semilinear Differential Inclusions of Order μ ∈ (1, 2) in Banach Spaces

Alsheekhhussain,

Ibrahim,

Al-Sawalha

et al. 2024

Fractal Fract

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“…In [4], based on the Guo-Krasnosel'skii fixed point theorem, the authors probed into the multiple positive solutions of a system of mixed Hadamard fractional BVP with (p 1 , p 2 )-Laplacian. In fact, some articles have been disposed of the BVP of p-Laplacian system involving Riemann-Liouville or Caputo fractional derivatives (see [5][6][7][8][9][10][11][12][13]).…”

Section: Introductionmentioning

confidence: 99%

“…In addition, we build the generalized Ulam-Hyers stability of system (1) based on nonlinear analysis methods and inequality techniques. (c) Many previous papers (see [2][3][4][5][6][7][8][9][10][11][12][13][17][18][19]24,25]) usually used some fixed-point theorems on Banach spaces to study the existence of solutions of fractional differential equations. However, we handle the existence of solutions to fractional order differential equations by defining two different distances on a complete distance space.…”

Section: Introductionmentioning

confidence: 99%

Solvability, Approximation and Stability of Periodic Boundary Value Problem for a Nonlinear Hadamard Fractional Differential Equation with p-Laplacian

Zhao

2023

Axioms

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The fractional order p-Laplacian differential equation model is a powerful tool for describing turbulent problems in porous viscoelastic media. The study of such models helps to reveal the dynamic behavior of turbulence. Therefore, this article is mainly concerned with the periodic boundary value problem (BVP) for a class of nonlinear Hadamard fractional differential equation with p-Laplacian operator. By virtue of an important fixed point theorem on a complete metric space with two distances, we study the solvability and approximation of this BVP. Based on nonlinear analysis methods, we further discuss the generalized Ulam-Hyers (GUH) stability of this problem. Eventually, we supply two example and simulations to verify the correctness and availability of our main results. Compared to many previous studies, our approach enables the solution of the system to exist in metric space rather than normed space. In summary, we obtain some sufficient conditions for the existence, uniqueness, and stability of solutions in the metric space.

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Study on the stability and its simulation algorithm of a nonlinear impulsive ABC-fractional coupled system with a Laplacian operator via F-contractive mapping

Zhao

2024

Adv Cont Discr Mod

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In this paper, we study the solvability and generalized Ulam–Hyers (UH) stability of a nonlinear Atangana–Baleanu–Caputo (ABC) fractional coupled system with a Laplacian operator and impulses. First, this system becomes a nonimpulsive system by applying an appropriate transformation. Secondly, the existence and uniqueness of the solution are obtained by an F-contractive operator and a fixed-point theorem on metric space. Simultaneously, the generalized UH-stability is established based on nonlinear analysis methods. Thirdly, a novel numerical simulation algorithm is provided. Finally, an example is used to illustrate the correctness and availability of the main results. Our study is a beneficial exploration of the dynamic properties of viscoelastic turbulence problems.

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Uniqueness of solutions for aψ-Hilfer fractional integral boundary value problem with thep-Laplacian operator

Abstract: In this article, we discuss the existence of a unique solution to a ψ \psi -Hilfer fractional differential equation involving the p p -L… Show more

Cited by 6 publications

References 30 publications

Mild Solutions for w-Weighted, Φ-Hilfer, Non-Instantaneous, Impulsive, w-Weighted, Fractional, Semilinear Differential Inclusions of Order μ ∈ (1, 2) in Banach Spaces

Mild Solutions for w-Weighted, Φ-Hilfer, Non-Instantaneous, Impulsive, w-Weighted, Fractional, Semilinear Differential Inclusions of Order μ ∈ (1, 2) in Banach Spaces

Solvability, Approximation and Stability of Periodic Boundary Value Problem for a Nonlinear Hadamard Fractional Differential Equation with p-Laplacian

Study on the stability and its simulation algorithm of a nonlinear impulsive ABC-fractional coupled system with a Laplacian operator via F-contractive mapping

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