【作者】 杨玲；

【导师】 蒋威； 周先锋；

【作者基本信息】 安徽大学 ， 应用数学， 2014， 硕士

【摘要】 由于现代工业的快速发展,人们为了更准确的描述、模拟实际现象引进了分数阶微分方程和分数阶微分系统.因此,对泛函微分系统、分数阶微分系统的研究有着重要的理论价值和实际意义.本文就分数阶微分系统的稳定性和能控性等问题作了一些讨论,并给出了一些结果.全文共分三章.第一章主要介绍分数微积分和分数微分系统的一些背景知识,给出本文所需的一些预备知识.第二章讨论了两类分数阶微分方程解的稳定性,利用推广的Gronwall不等式给出了解稳定的几个充分条件.第三章讨论了一类具有Riemann-Liouville分数阶导数的线性时不变微分系统的完全能控性,并给出了相应的能控性充要条件.更多还原

【Abstract】 Modern industries develop rapidly, fractional calculus and fractional differential e-quations were introduced in order to describle and model the practical phenomena more exactly. Thus there are much theoretical value and practical meaning of the research on functional differential equations and fractional differential systems.In this paper, the stability and the controllability of several fractional differential systems are discussed and many results are also given. There are three chapters in this paper.In the first chapter, some background knowledge of fractional calculus and fractional differential systems are introduced, and the preliminary knowledge which is necessary in the paper is given.In the second chapter, we discuss the stability of two classes of fractional order dif-ferential equations. Some sufficient conditions that guarantee the stability of the solutions are given by using generalized Gronwall inequality.In chapter3, we discuss the complete controllability of a fractional linear time-invariant differential system with Riemann-Liouville derivative. And we obtain necessary and sufficient conditions of the controllability.更多还原