The Existence Of Solutions For Boundary Value Problem Of Fractional Order Impulsive Differential Equations

With the development of the times, the mathematical model of the differential equations has been used widely. The research of differential equations is also increasing. A class of impulsive differential equations is an important problem, and also attract more and more scholars. Integer order impulsive differential equation boundary value problems have got great academic achievements, but, relatively speaking, the research of the boundary value problem of fractional order impulsive differential equations is relatively short. In this essay I will focus on the three kinds of boundary value problem of fractional order impulsive differential equations.In the first chapter, it is the introduction, this paper briefly describes the time background of differential equation, development present situation and development prospect.In the second chapter, the boundary value problem of fractional order impulsive differential equations systems are studied. By defining a suitable linear space and norm, giving the appropriate operator, under the nonlinear term and pulse values satisfy certain conditions, using image compression theory and Krasnoselskii fixed point theorem respectively, I can get the existence and uniqueness of the boundary value problem of fractional order impulsive differential equations systems.In the third chapter, it is further studied for the boundary value problems of fractional order impulsive differential equations. Boundary conditions of the original equation changes so that the equation becomes more general. Then by applying the fixed point theorem conclusions of original equations are further promotion, so the results becomes more general.In the fourth chapter, it is studied the boundary value problems of fractional order impulsive differential equations with P-Laplacian operator. By defining a suitable linear space and norm, then giving the appropriate operator, under the condition satisfies the equations, the application of Schauder fixed point theorem, I get the existence of solutions for the boundary value problems of fractional order impulsive differential equations with P-Laplacian operator.