| 时不变和时变的Caputo分数阶时滞微分系统的常数变易公式 |
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| 引用本文： | 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 |
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| 作者姓名： | 张海 伍代勇 |
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| 作者单位： | 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;安庆师范学院数学系, 安徽 安庆 246011 |
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| 基金项目： | 安徽省高等学校自然科学基金项目(Grant No.KJ2011A197). |
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| 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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| 关 键 词： | 时滞微分系统 线性时间 分数阶 公式 延迟微分方程 Gronwall 线性时不变 时变 |
| 收稿时间： | 2013-10-22 |
| 修稿时间： | 2014-03-20 |
Variation of Constant Formulae for Time Invariant and Time Varying Caputo Fractional Delay Differential Systems |
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| Hai ZHANG and Daiyong WU. Variation of Constant Formulae for Time Invariant and Time Varying Caputo Fractional Delay Differential Systems[J]. Journal of Mathematical Research with Applications, 2014, 34(5): 549-560 |
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| Authors: | Hai ZHANG and Daiyong WU |
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| Affiliation: | Department of Mathematics, Anqing Normal University, Anhui 246133, P. R. China; Department of Mathematics, Southeast University, Jiangsu 210096, P. R. China;Department of Mathematics, Anqing Normal University, Anhui 246133, P. R. China |
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| Abstract: | 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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| Keywords: | fractional delay differential systems variation formula exponential estimates Laplace transform Gronwall's integral inequality. |
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