Existence Of Solutions Of Integral Boundary Value Problems For Two Singular Fractional Differential Equations

Fractional differential equation is a discipline developed along with the fractional calculus.It plays an important role in many fields such as physics,electrical circuits,biology,control theory,etc.Based on the universality and validity of its application,it is of great theoretical significance and practical application value for the study of fractional calculus and fractional differential equations.In this thesis,we study the existence of positive solutions for two singular nonlinear fractional differential equations,by using Guo-Krasnoselskii fixed point theory of nonlinear functional analysis and theorem of Leray Schauder degree.The existence of solutions to boundary value problems of two kinds of singular fractional differential equations is Proved,and some new profound and meaningful results are obtained.This thesis is divided into four chapters.The specific contents are as follows:Chapter 1 is the introduction,which briefly introduce the nonlinear functional analy-sis and the historical background of fractional differential equations and shows some basic definitions and properties of nonlinear functional analysis theory.And it lists several lem-mas about the existence of fixed points that are used in the following sections,the lemmas is critical in this paper.In chapter 2,by using a special space and Guo-Krasnoselskii fixed point theorem on cone and the method of Green's function,we obtain existence results of positive solution for a class of singular boundary value problems.The nonlinear term has singularity,which brings some difficulties to our derivation.In this case,we extend and improving the exist-ing results.In chapter 3,we consider the existence of positive solutions for a class of singu-lar fractional differential equations involving a P-laplacian operator.Based on Leray-Schauder theory,some new results are obtained.Chapter 4 is devoted to summarization and prospect.