Existence Of Solutions Of Fractional Impulsive Differential Equations

The theory of functional differential equations has emerged as an important branch of nonlinear analysis, nonlinear differential equations with integral boundary value conditions and systems of nonlinear differential equations are one of most active domains of functional analysis studies at present. In this paper,we use contraction mapping principle, the Krasnoselskii’s fixed point theorem,Schaefer fixed point theorem, combined with Guo-Krasnosel’skii fixed point theorem to study the existence and uniqueness of positive solutions for fractional differential equations.The thesis is divided into three chapters according to contents. In Chapter1, we study the existence of solutions for impulsive fractional integro-differential equations of order ∈(1, 2) with integral conditions by the application of the Banach contraction mapping principle and the Krasnoselskii’s fixed point theorem and the Schaefer fixed point theorem.(?)This chapter mainly generalizes the paper[25]in equation form and the boundary conditions. The problem studied by the paper[25] is a special case of this paper, for the paper[1], we mainly make some corresponding promotions in equation form, the boundary conditions and the impulses.In Chapter 2, we study the existence of solutions for the following impulsive fractional differential equations.(?)The results are established by the application of the Banach contraction mapping principle and the Krasnoselskii’s fixed point theorem, this chapter mainly generalizes the paper [24]in the boundary conditions, and makes the promotion to the system of equations.In Chapter 3 we study the existence of positive solutions for fractional impulsive differential equations with boundary value conditions,(?)Under different combinations of superlineary and sublineary of nonlinear term and the impulses, various existence, multiplicity and nonexistence results for positive solutions are derived in terms of the parameter lies in some intervals by the application of Guo-Krasnosel’skii fixed point theorem on cones. The chapter introduces the parameter for the nonlinear term of the paper [30], we increase research of singularity about (8(), = 0, 1.