Existence Of Solutions For Three Kinds Of Fractional Differential Equations Boundary Value Problems

The research of the boundary value problems for fractional differential equation with a wide range of theoretical and practical significance,has been widely concerned.Along with the development of science and technology,the boundary value problem for fractional differential equations has been widely applied in the emergency disciplines,such as physics,chemistry,medicine and other fields.As the special cases of fractional nonlocal boundary value problems,the boundary value problems for fractional differential equations at resonance have arisen the attention of numerous scholars.In this thesis,the Mawhin continuation theorem of coincidence degree theory,the fixed point theorem and other theories are used to investigate the existence of positive solutions for three kinds of differential equation boundary value problems at resonance or non-resonance.This thesis draws a conclusion of the solution for the boundary value problems with new conditions.In Chapter 1,we mainly introduce the background of the research and research status of fractional differential equations boundary value problems,and the main content of this thesis.In Chapter 2,a sufficient condition for the existence of solutions of four-point boundary value problem for fractional differential equations at resonance is established by weakening the boundary conditions.The conclusions of this chapter enrich the existing research results.In Chapter 3,this thesis studies the fractional differential equations boundary value problem with integral boundary condition at resonance on the half-line by using the coincidence degree theory,where the non-linear item is more general.The results of this chapter construct the appropriate norm spaces and projector operators,and study the existence of solutions for this boundary value problem.In Chapter 4,this thesis studies the fractional differential equations three-point boundary value problem by using the contraction mapping principle and fixed point theorem in partially ordered sets.Besides,it also discusses the existence and uniqueness of positive solutions and proves the monotonicity of positive solutions.In Chapter 5,this chapter is about the major findings and the limitations of this thesis as well as the suggestions for further studies.