Lyapunov Stability And Asymptotical Stability Of Nonlinear Fractional Order Differential Systems With(0,1) Order

Stability and asymptotic stability of nonlinear differential systems is an old subject,which has important engineering value. Based on the Fractional Calculus appearing in a number of application areas, we primarily take the advantage of Lyapunov-class methods and comparative principles to study the stability and asymptotic stability of different orders of non-autonomous nonlinear fractional differential system, and then made a number of simple and convenient method to study stability and asymptotic stability of autonomous and nonautonomous differential system in the article.The thesis is divided into six chapters:In chapter 1, we give the background, the present situation and the development trend of research on Lyapunov stability and asymptotical stability of nonlinear fractional order differential systems with(0,1) order and the main research of this thesis.In chapter 2, we introduce the necessary preliminaries such as definitions, properties of fractional calculus and some related lemmas and so on.In chapter 3, we discuss stability and asymptotic stability of a class of different order’s nonlinear non-autonomous fractional differential systems by applying the Lyapunov method and comparison principles, Under some suitable assumptions, new results to determine the stability and asymptotic stability of the system are obtained,which extends part of the previous work.In chapter 4,we present a simpler and more convenient way to determine the stability and asymptotic stability of a class of nonlinear fractional differential autonomous system from the application perspective. By applying fractional comparison principles,the Leibniz rule of fractional derivatives and Gronwall inequality of fractional order, we obtain some new results to analyse the stability and asymptotic stability of the solutions of the system.In chapter 5,we study the stability and asymptotic stability of the nonlinear fractional differential non-autonomous system solution from a practical point, and propose a method to determine the stability and asymptotic stability of the system under appropriate assumptions.In chapter 7, we make a brief summary for this paper and introduce our future work.