分数阶非线性时滞脉冲微分系统的全局Mittag-Leffler稳定性

数学物理学报 ›› 2020, Vol. 40 ›› Issue (4): 1053-1060.

分数阶非线性时滞脉冲微分系统的全局Mittag-Leffler稳定性

刘健(),张志信*(),蒋威()

^{安徽大学数学科学学院合肥 230601}

收稿日期:2019-01-31 出版日期:2020-08-26 发布日期:2020-08-20
通讯作者: 张志信 E-mail:1916869562@qq.com;zhang_zhi_x@sina.com;jiangwei@ahu.edu.cn
作者简介:刘健, E-mail:1916869562@qq.com|蒋威, E-mail:jiangwei@ahu.edu.cn
基金资助:
国家自然科学基金(11371027);国家自然科学基金(11471015);国家自然科学基金(11601003);安徽省自然科学基金(1608085MA12);安徽省自然科学基金(2008085QA19)

Global Mittag-Leffler Stability of Fractional Order Nonlinear Impulsive Differential Systems with Time Delay

Jian Liu(),Zhixin Zhang*(),Wei Jiang()

^{School of Mathematical Sciences, Anhui University, Hefei 230601}

Received:2019-01-31 Online:2020-08-26 Published:2020-08-20
Contact: Zhixin Zhang E-mail:1916869562@qq.com;zhang_zhi_x@sina.com;jiangwei@ahu.edu.cn
Supported by:
the NSFC(11371027);the NSFC(11471015);the NSFC(11601003);the NSF of Anhui Province(1608085MA12);the NSF of Anhui Province(2008085QA19)

摘要/Abstract

摘要：

该文主要研究了含有脉冲和时滞因素的分数阶非线性微分系统的全局Mittag-Leffler稳定性.利用分数阶Lyapunov方法和Mittag-Leffler函数性质，给出了含有脉冲时滞分数阶非线性微分系统全局Mittag-Leffler稳定性的充分条件，然后用具体的例子证明了所得结果的有效性.

关键词: 分数阶非线性微分系统, 时滞, 全局Mittag-Leffler稳定性, 脉冲, Lyapunov方法

Abstract:

In this paper, the global Mittag-Leffler stability of fractional-order nonlinear differential systems with impulsive and time-delay factors is studied. By using the fractional Lyapunov method and Mittag-Leffler function, sufficient conditions for global Mittag-Leffler stability of fractional-order nonlinear differential systems with impulsive time-delay are given. Finally, an example is given to demonstrate the effectiveness of the results.

Key words: Fractional-order nonlinear differential system, Time delay, Global Mittag-Leffler stability, Impulse, Lyapunov method

中图分类号:

O175.15

刘健,张志信,蒋威. 分数阶非线性时滞脉冲微分系统的全局Mittag-Leffler稳定性[J]. 数学物理学报, 2020, 40(4): 1053-1060.

Jian Liu,Zhixin Zhang,Wei Jiang. Global Mittag-Leffler Stability of Fractional Order Nonlinear Impulsive Differential Systems with Time Delay[J]. Acta mathematica scientia,Series A, 2020, 40(4): 1053-1060.

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