Existence And Stability Of Solutions For Impulsive Fractional Differential Equations

In this paper,we study the existence of the solution of the Dirichlet bound-ary value problem for a class of mixed left and right Riemann-Liouville impulsive fractional differential equations with perturbations,and the stability of the so-lution of the initial value problem for a class of impulsive fractional differential equation with perturbations.This paper consists four chapters.In chapter 1,we introduce the background and the research status of frac-tional differential equations and impulsive differential equations,and then the main contents of this dissertation are also outlined.In chapter 2,some basic definitions and theorems used in this paper are given,including fractional calculus,critical point theory,and so on.In chapter 3,by using some theorems of critical point theory such as mini-mization,mountain pass theorem,symmetric mountain pass lemma and so on,we give the sufficient conditions to guarantee the existence of at least one,at least two and infinitely many solutions for the Dirichlet boundary value prob-lem.In chapter 4,several sufficient conditions for stability,uniform stability,asymptotical stability,Mittag-Leffler stability and generalized Mittag-Leffler stability,based on Lyapunov-like method and comparison principle,are estab-lished.