Existence and Ulam Type Stability for Impulsive Fractional Differential Systems with Pure Delay

Chen, Chao-Wen; Li, Mengmeng

doi:10.3390/fractalfract6120742

Cited by 4 publications

(2 citation statements)

References 34 publications

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“…Since then, Hyers [8] refined the Ulam-Hyers stability, and Rassias [9] further developed the Ulam-Hyers-Rassias stability. At present, researchers have made progress in studying the existence and Ulam stability analysis of fractional differential equations (see [10][11][12][13][14]). We note that there are few results on fractional differential equations with multiple terms.…”

Section: Introductionmentioning

confidence: 99%

The Existence and Ulam Stability Analysis of a Multi-Term Implicit Fractional Differential Equation with Boundary Conditions

Wang,

Han,

Bao

2024

Fractal Fract

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In this paper, we investigate a class of multi-term implicit fractional differential equation with boundary conditions. The application of the Schauder fixed point theorem and the Banach fixed point theorem allows us to establish the criterion for a solution that exists for the given equation, and the solution is unique. Afterwards, we give the criteria of Ulam–Hyers stability and Ulam–Hyers–Rassias stability. Additionally, we present an example to illustrate the practical application and effectiveness of the results.

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Section: Introductionmentioning

confidence: 99%

The Existence and Ulam Stability Analysis of a Multi-Term Implicit Fractional Differential Equation with Boundary Conditions

Wang,

Han,

Bao

2024

Fractal Fract

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“…Subsequently, extensive and in-depth research was conducted on the Ulam-Hyers stability of various systems. Especially, many excellent research results have emerged regarding the Ulam-Hyers stability of fractional order differential systems (see some of them [3,21,[24][25][26][27][28][29][30][31][32]). Moreover, it is rare to combine the Hadamard fractional derivative with Laplacian operator.…”

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

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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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Existence and Ulam Type Stability for Impulsive Fractional Differential Systems with Pure Delay

Cited by 4 publications

References 34 publications

The Existence and Ulam Stability Analysis of a Multi-Term Implicit Fractional Differential Equation with Boundary Conditions

The Existence and Ulam Stability Analysis of a Multi-Term Implicit Fractional Differential Equation with Boundary Conditions

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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