Existence Of Positive Solutions For Integral Boundary Value Problems Of Fractional Differential Equations

In this paper, by applying Krasnoselskii's fixed point theorems, Leray-Schauder nonlinear alternative theorem and fixed point index theorem, we study three types of fractional differential equations with semipositone, in-finite and singular integral boundary conditions, and obtain some new existence results.The theses is divided into four chapters altogether. The first chapter is introduction the history and evolution of fractional differential equation with integral boundary conditions, the relevant definitions, theorems, pro-perties and some fixed point theorems are given.In the second chapter, we study the existence of positive solution for a class of semipositone fractional differential equations with integral boundary conditions. We gave the corresponding Green's function for the coupled systems and its properties. Moerover, using Krasnoselskii's fixed point theorems, the existence of positive solution is acquired. At last, an example is given to confirm the application value of our main results.In the third chapter, by establishing appropriate Banach space and compactness criterion, applying of Leray-Schauder nonlinear alternative theorem, we obtain unbounded solution of integral boundary condition with p-Laplacian operator on the half line.In the last chapter, through fixed point index theorem and monotone iterative techniques, we consider a singular differential equation with in-tegral boundary value problem.