A stability criterion for fractional-order complex-valued differential equations with distributed delays. (November 2021)

• Record Type: Journal Article
• Authors: Yao, Zichen; Yang, Zhanwen; Zhang, Yusong
• Is Part Of: Chaos, solitons and fractals. Volume 152(2021)
• Publication Date: 2021-11
• Subjects: Complex-valued differential equations -- Caputo's fractional derivative -- Stability -- Laplace transform -- Time delays; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2021.111277
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: A novel necessary and sufficient condition for the stability is expressed in an easily verified algebraical criterion. The Laplace transform method and a method of imbedding the characteristic equation are used. Our results yield a delay independent stability condition for discrete delays, which coincides with the well-known real-valued differential equations. For fractional-order complex-valued integro-differential equation, the stability criterion is delay-dependent. Abstract: In this paper, we investigate the global asymptotic stability of fractional-order complex-valued differential equations with distributed delays. Based on the Laplace transform method, a novel necessary and sufficient condition for the stability is established by imbedding the characteristic equation into two-dimensional complex system. The algebraical criterion is expressed by the fractional exponent, coefficients and the delay. Finally, two numerical examples are given to show the feasibility and effectiveness of the theoretical results.