张海,伍代勇.时不变和时变的Caputo分数阶时滞微分系统的常数变易公式[J].数学研究及应用,2014,34(5):549~560
时不变和时变的Caputo分数阶时滞微分系统的常数变易公式
Variation of Constant Formulae for Time Invariant and Time Varying Caputo Fractional Delay Differential Systems
投稿时间:2013-10-22  最后修改时间:2014-03-20
DOI:10.3770/j.issn:2095-2651.2014.05.006
中文关键词:  分数阶时滞微分系统  变易公式  指数估计  Gronwall积分不等式  Laplace变换.
英文关键词:fractional delay differential systems  variation formula  exponential estimates  Laplace transform  Gronwall's integral inequality.
基金项目:安徽省高等学校自然科学基金项目(Grant No.KJ2011A197).
作者单位
张海 安庆师范学院数学系, 安徽 安庆 246011; 东南大学数学系, 江苏 南京 210096 
伍代勇 安庆师范学院数学系, 安徽 安庆 246011 
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中文摘要:
      本文讨论了时不变和时变的Caputo分数阶时滞微分系统的常数变易公式.通过Gronwall积分不等式对时不变的Caputo分数阶时滞微分系统进行了解的指数估计,利用Laplace变换得到其常数变易公式;根据线性系统的迭代原理和基本解矩阵,建立了时变的Caputo分数阶时滞微分系统的常数变易公式.所得结果推广了整数阶时滞微分系统的变易公式.
英文摘要:
      This paper studies the variation of constant formulae for linear Caputo fractional delay differential systems. We discuss the exponential estimates of the solutions for linear time invariant fractional delay differential systems by using the Gronwall's integral inequality. The variation of constant formula for linear time invariant fractional delay differential systems is obtained by using the Laplace transform method. In terms of the superposition principle of linear systems and fundamental solution matrix, we also establish the variation of constant formula for linear time varying fractional delay differential systems. The obtained results generalize the corresponding ones of integer-order delayed differential equations.
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