Some results on finite-time stability of stochastic fractional-order delay differential equations. (May 2022)

• Record Type: Journal Article
• Authors: Luo, Danfeng; Tian, Mengquan; Zhu, Quanxin
• Is Part Of: Chaos, solitons and fractals. Volume 158(2022)
• Publication Date: 2022-05
• Subjects: Stochastic differential equation -- Fractional calculus -- Finite-time stability -- Laplace transformation; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.111996
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: Finite-time stability of stochastic fractional-order delay differential equations is researched here. Firstly, we derive the equivalent form of the considered system by using the Laplace transformation and its inverse. Subsequently, by defining the maximum weighted norm in Banach space and using the principle of contraction mapping, we prove that the solution of researched system is unique. What's more, by virtue of Henry-Grönwall delay inequality and interval translation, we derive the criterion of finite-time stability for the system with and without impulses, respectively. Finally, as a verification, examples are provided to expound the correctness of the deduced results.