Existence Of Solutions Of Fractional Differential Equations And Boundary Value Problems With P-laplacian Operators

Firstly, we describe the basic background of this dissertation in preface.Secondly, in the first chapter we give some related knowledge of the fractional integrals and the fractional order differential.And then in the second chapter,when 1< a≤2, we study the existence and uniqueness of the solutions to m-point boundary value problem of fractional differentialThe next few chapters we will pay attention to studying the solution to the boundary value problem of several types of nonlinear fractional differential equations including p-Laplacian operator.In the third chapter, when 2< a≤3,by using the Banach contraction mapping principle and the cone is not fixed point theorem, we can study the existence and uniqueness of a type of the boundary value problem of differential equationsIn the fourth chapter,when 2< a≤ 3,the first half of this chapter, by using the properties of the Green function, bounded function, the fixed point index theory and the fixed point theorem of cone expansion and compression, we will study the existence of the solutions to the fractional differential equations, which is a class of p-Laplacian operators and integral boundary conditions where. In the latter part of this chapter, with the utilization of Kranoselskii fixed point theorem, we study the existence for positive solutions of one class singular equation’s boundary value problem with p-Laplacian operator when the equation is pesitone and semipesitone respectivelyIn the fifth chapter, when n-1<a≤n,taking advantage of nonlinear term’s height function on bound set and Kranoselskii Fixed point theorem, we will research one class of infinite point boundary value problem,which obtain the existence of multiplicity of positive solutions and examine the efficiency for the results via examples.