Stability And Controllability Of Fractional Order Differential Equations

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.