Existence and Finite-Time Stability Results for Impulsive Caputo-Type Fractional Stochastic Differential Equations with Time Delays

Tian, Mengquan; Luo, Danfeng

doi:10.1515/ms-2023-0030

Mathematica Slovaca

2023

DOI: 10.1515/ms-2023-0030

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Existence and Finite-Time Stability Results for Impulsive Caputo-Type Fractional Stochastic Differential Equations with Time Delays

Mengquan Tian

Danfeng Luo

Abstract: This paper mainly discusses the existence and finite-time stability of solutions for impulsive fractional stochastic differential equations (IFSDEs). By applying the Picard-Lindelöf iteration method of successive approximation scheme, we establish the existence results of solutions. Subsequently, the uniqueness of solution is derived by the method of contradiction. In addition, we investigate the finite-time stability by means of the generalized Grönwall-Bellman inequality. As an application, examples are prov… Show more

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Cited by 8 publications

References 48 publications

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Finite‐time stability and numerical approximations of fractional neutral delay systems involving proportional Caputo derivative

Makhlouf,

Nagy

2024

Math Methods in App Sciences

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This paper deals with a class of fractional neutral delay systems involving proportional Caputo derivative. Maintaining the finite‐time stability of fractional‐order systems is a major challenge, as their capacity to mimic complex dynamics draws more attention to them. Therefore, the paper presents a novel finite‐time stability criterion based on the Banach fixed‐point theorem. A decomposition formula for proportional Caputo derivative is provided. This formula allows us to derive a new numerical technique for efficiently solving the proposed problem. Finally, extensive numerical results are performed to illustrate and validate the proposed theoretical results.

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Finite‐time stability and numerical approximations of fractional neutral delay systems involving proportional Caputo derivative

Makhlouf,

Nagy

2024

Math Methods in App Sciences

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Relatively exact controllability of fractional stochastic neutral system with two incommensurate constant delays

Yuan,

Luo

2024

Math Methods in App Sciences

Self Cite

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This paper is devoted to analyzing a kind of fractional stochastic neutral system (FSNS). Firstly, by introducing the notion of newly defined two‐parameter Mittag–Leffler matrix function, we derive the solution of the corresponding linear stochastic system. Subsequently, for the linear case, by virtue of the Grammian matrix, we give a suffcient and necessary condition to guarantee the relatively exact controllability for the addressed case. Furthermore, for the nonlinear one, the relatively exact controllability is obtained by fixed point and explore it via Banach contraction principle. Finally, two examples are provided to intensify our theoretical conclusions.

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A hybrid yang transform adomian decomposition method for solving time-fractional nonlinear partial differential equation

Bekela,

Deresse

2024

BMC Res Notes

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Nonlinear time-fractional partial differential equations (NTFPDEs) play a great role in the mathematical modeling of real-world phenomena like traffic models, the design of earthquakes, fractional stochastic systems, diffusion processes, and control processing. Solving such problems is reasonably challenging, and the nonlinear part and fractional operator make them more problematic. Thus, developing suitable numerical methods is an active area of research. In this paper, we develop a new numerical method called Yang transform Adomian decomposition method (YTADM) by mixing the Yang transform and the Adomian decomposition method for solving NTFPDEs. The derivative of the problem is considered in sense of Caputo fractional order. The stability and convergence of the developed method are discussed in the Banach space sense. The effectiveness, validity, and practicability of the method are demonstrated by solving four examples of NTFPEs. The findings suggest that the proposed method gives a better solution than other compared numerical methods. Additionally, the proposed scheme achieves an accurate solution with a few numbers of iteration, and thus the method is suitable for handling a wide class of NTFPDEs arising in the application of nonlinear phenomena.

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Existence and Finite-Time Stability Results for Impulsive Caputo-Type Fractional Stochastic Differential Equations with Time Delays

Cited by 8 publications

References 48 publications

Finite‐time stability and numerical approximations of fractional neutral delay systems involving proportional Caputo derivative

Finite‐time stability and numerical approximations of fractional neutral delay systems involving proportional Caputo derivative

Relatively exact controllability of fractional stochastic neutral system with two incommensurate constant delays

A hybrid yang transform adomian decomposition method for solving time-fractional nonlinear partial differential equation

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