The Existence Of Solutions Of Boundary Value Problem For Several Kinds Of Fractional Differential Equations

The theory of boundary value problem for fractional differential equation has been constantly enriched and more and more widely used, so the boundary value problem of fractional differential equation becomes a critical research issue for many scholars. It also makes the boundary value problem to promote.In this paper we consider some of fractional differential equations in different boundary conditions. We obtain the existence of solution, positive solution for the boundary value problems.This paper is organized as follows:In the first chapter,we consider the boundary value problems of the research status for fractional differential equation at home and abroad, make the review of historical background of the issue in this paper.Finally,we elaborate the main results we get.In the second chapter,we study the boundary value problems of fractional differential equations with integral boundary condition. Using the Leggett-Williams fixed point theorem, we obtain the existence of multiple positive solutions of the boundary value problems.In the third chapter, we discuss the boundary value problem of fractional differential equation with a parameter,we construct a Green function.Through the use of properties of the Green function and the expansion and compression fixed point theorem, we obtain the existence of positive solutions of the boundary value problems.In the fourth chapter, mainly using the Banach contraction mapping principle and Krasnoselskii fixed point theorem, we consider a class of infinite boundary value problem for fractional differential equation, we obtain the existence of unique solution and at least one solution of the boundary value problems.