Asymptotic stability of a periodic GA-predation system with infinite distributed lags on time scales

Zhao, Kaihong

doi:10.1080/00207179.2023.2214251

Cited by 4 publications

(1 citation statement)

References 70 publications

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“…Only a small number of published papers deal with the solvability and stability of implicit Hadamard fractional differential equations (see [48][49][50][51][52][53][54][55][56]). Some academic researchers have applied the theory of coincidence degree to study the solvability of integer-order nonlinear functional differential equations and have achieved fruitful results (see [57][58][59][60][61][62][63][64][65][66][67][68]). In the theory of coincidence degree, the construction of relevant operators is highly skilled, which brings difficulties to the application of this method.…”

Section: Remark 2 When Boundary Conditionsmentioning

confidence: 99%

A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory

Zhao,

Liu,

2024

Fractal Fract

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The Langevin equation is a model for describing Brownian motion, while the Sturm–Liouville equation is an important mechanical model. This paper focuses on the solvability and stability of nonlinear impulsive Langevin and Sturm–Liouville equations with Caputo–Hadamard (CH) fractional derivatives and multipoint boundary value conditions. To unify the two types of equations, we investigate a general nonlinear impulsive coupled implicit system. By cleverly constructing relevant operators involving impulsive terms, we establish the coincidence degree theory and obtain the solvability. We explore the stability of solutions using nonlinear analysis and inequality techniques. As the most direct application, we naturally obtained the solvability and stability of the Langevin and Sturm–Liouville equations mentioned above. Finally, an example is provided to demonstrate the validity and availability of our major findings.

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Section: Remark 2 When Boundary Conditionsmentioning

confidence: 99%

A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory

Zhao,

Liu,

2024

Fractal Fract

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Generalized UH-stability of a nonlinear fractional coupling $(\mathcalligra{p}_{1},\mathcalligra{p}_{2})$-Laplacian system concerned with nonsingular Atangana–Baleanu fractional calculus

Zhao

2023

J Inequal Appl

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The classical $\mathcalligra{p}$ p -Laplace equation is one of the special and significant second-order ODEs. The fractional-order $\mathcalligra{p}$ p -Laplace ODE is an important generalization. In this paper, we mainly treat with a nonlinear coupling $(\mathcalligra{p}_{1},\mathcalligra{p}_{2})$ ( p 1 , p 2 ) -Laplacian systems involving the nonsingular Atangana–Baleanu (AB) fractional derivative. In accordance with the value range of parameters $\mathcalligra{p}_{1}$ p 1 and $\mathcalligra{p}_{2}$ p 2 , we obtain sufficient criteria for the existence and uniqueness of solution in four cases. By using some inequality techniques we further establish the generalized UH-stability for this system. Finally, we test the validity and practicality of the main results by an example.

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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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Asymptotic stability of a periodic GA-predation system with infinite distributed lags on time scales

Cited by 4 publications

References 70 publications

A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory

A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory

Generalized UH-stability of a nonlinear fractional coupling $(\mathcalligra{p}_{1},\mathcalligra{p}_{2})$-Laplacian system concerned with nonsingular Atangana–Baleanu fractional calculus

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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