Existence Of Solutions For Two Classes Of Nonlinear Fractional Differential Equation Boundary Value Problems

In this paper,we discuss the existence of positive solutions of two classes of nonlin-ear fractional differential equation boundary value problems.This paper mainly includes the following four chapters:In chapter 1,this part introduce the backgrounds and the development process of the problem,the equations to be studied are given.In chapter 2,the concepts of fractional integral,fractional derivative and Mittag-Leffler function are given to facilitate the interpretation of this paper.In chapter 3,this part mainly study the following fractional differential equation:#12 where ?p=|u|p-2,p<1,2<?,??3,5 ??+?? 6,By using properties of Green function and the Guo-Krasnosel' skii fixed point theorem,we obtain the existence of the solution of the boundary value problem,As an extension,the paper consider the multiplicity of the solution of the following differential equations:#12 where ? is a positive parameter.In chapter 4,this part mainly study the following fractional differential equation:#12 where ??0,f:[0,1]×[0,?)?·[0,?)is continuous function.According to the formal solution,the expression form of the solution of the equation is obtained,the green's function is studied,and the necessary properties are obtained.Finally,several methods of fixed-point theorem and monotone iteration are applied,the existence and uniqueness of solution of boundary value problem are obtained,and some examples are given.