中国科学技术大学学报 ›› 2015, Vol. 45 ›› Issue (8): 633-637.DOI: 10.3969/j.issn.0253-2778.2015.08.003
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张 海
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ZHANG Hai
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摘要： 主要讨论混合型分数阶线性多时滞微分方程通解表示问题. 基于Gronwall-Bellman积分不等式获得该方程解的指数估计, 利用线性齐次微分方程的基础解和Laplace变换导出齐次方程的通解, 利用Laplace逆变换和卷积定理获得非齐次方程的通解表达式.
关键词: 混合型分数阶线性系统, 多时滞, 基础解, 通解, 拉普拉斯变换
Abstract: The representation problem of general solutions of hybrid linear fractional-order differential systems with multiple time delays was discussed. Based on Gronwall-Bellman integral inequality, the exponential estimates of the solutions of this equation were derived. The general solution to hybrid linear homogeneous fractional-order differential equations with multiple time delays was derived by means of the fundamental solution of the homogeneous systems and the Laplace transform method, then the general solution of the nonhomogeneous systems was obtained by means of Laplace inverse transform and convolution theorem.
Key words: hybrid fractional-order linear systems, multiple time delays, fundamental solution, general solution, Laplace transform
张 海，李 琳，蒋 威. 具多时滞的混合型分数阶微分方程的通解表示[J]. 中国科学技术大学学报, 2015, 45(8): 633-637.
ZHANG Hai, LI Lin, JIANG Wei. Representation of general solutions to hybrid fractional-order differential equations with multiple time delays[J]. Journal of University of Science and Technology of China, 2015, 45(8): 633-637.
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http://just-cn.ustc.edu.cn/CN/Y2015/V45/I8/633
