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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2018, Vol. 35 ›› Issue (1): 45-54.doi: 10.3969/j.issn.1005-3085.2018.01.005

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分数阶退化时滞微分系统的稳定性问题

张志信,   张玉峰,   蒋   威   

  1. 安徽大学数学科学学院，合肥  230601
  • 收稿日期:2015-12-28 接受日期:2016-12-13 出版日期:2018-02-15 发布日期:2018-04-15
  • 基金资助:
    国家自然科学基金(11371027; 11471015; 11601003)；安徽省自然科学基金(1608085MA12)；高等学校博士点专项科研资助基金(20123401120001)；安徽大学博士科研启动经费资助项目(023033190142)；安徽大学研究生学术创新研究扶持与强化项目(yfc100013).

The Problem of Stability of Fractional Degenerate Differential System with Delay

ZHANG Zhi-xin,   ZHANG Yu-feng,   JIANG Wei   

  1. School of Mathematical Sciences, Anhui University, Hefei 230601
  • Received:2015-12-28 Accepted:2016-12-13 Online:2018-02-15 Published:2018-04-15
  • Supported by:
    The National Natural Science Foundation of China (11371027; 11471015; 11601003); the Natural Science Foundation of Anhui Province (1608085MA12); the Doctoral Program Foundation of Ministry of Education of China (20123401120001); the Research Fund for the Doctoral Program of Anhui University (023033190142); the Research and Support Program for Innovation of Graduate Students of Anhui University (yfc100013).

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摘要： 本文主要研究了含有退化和时滞因素的分数阶微分系统的稳定性．首先，利用分数阶Laplace变换讨论了在Caputo分数阶导数意义下的具有不同分数阶导数的多时滞退化微分系统的稳定性条件，并且对于不同的情况给出了相应的判别方法．其次，利用特征方程的根的分析结果研究了分数阶退化时滞微分系统的全时滞稳定性问题，给出了判定该系统全时滞稳定的充分性条件，获得的结果推广了相关文献的结论．最后给出了具体例子说明了定理条件的有效性．

关键词: 稳定性, 退化微分方程, 分数阶, 时滞

Abstract: The stability of a fractional degenerate differential system with delay is considered. Firstly, according to the Laplace transform method for the Caputo fractional derivatives, the stability conditions for the degenerate differential system with multiple-delays under different Caputo derivatives are derived and the corresponding criterions are given in different cases. Secondly, by using the roots of the characteristic equation, the all-delays stability of fractional degenerate differential systems are analyzed and some sufficient conditions are obtained. Some results generalize the corresponding results of the fractional differential system. Finally, some examples are presented to illustrate the validity of theorems.

Key words: stability, degenerate differential equation, fractional order, delay

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