The Existence Of Solutions For Boundary Value Problem Of Fractional Differentialequations On Infinite Interval

The fractional differential equation boundary value problem on the infinite interval is one of the main branches of differential equation problem.Its main characteristics are the very wide research area and wide application background,such as radial symmetric nonlinear elliptic equations and half infinite porous medium pressure model,electrostatic measurement of solid propulsion fuel in rocket exhaust pipes,nonlinear mechanics,etc.This paper studies three types for boundary value problems of fractional differential equations on infinite interval.Combining with each type of fractional differential equation boundary value problem of the nature of the green's function and using research methods like0)?6-?8??6?90?nonlinear choice,0?2?2?0)-?24?7)7)4)?68?fixed point theorem,Cone compression and Cone expansion fixed point theorem and other research methods.This research finds out that the existence of solutions for three kinds boundary value problem of fractional differential equations on infinite interval.This paper is divided into five chapters,the main contents are arranged as following:In the first chapter,this thesis studies the background and current situation of fractional differential equations,introduces the main research contents and research methods,and gives the preliminary knowledge needed in this thesis.In the second chapter,this thesis studies a class of fractional three-point boundary value problems on infinite interval.According to the properties of the non-linear item?6??1??,???,this chapter assumes some constraints to study the existence of at least one solution and at least three solutions of the system by using the0)?6-?8??6?90?fixed point theorem and0?2?2?0)-?24?7)7)4)?68?fixed point theorem.Compared to the results of[36,41],the results in this chapter is more general.In the third chapter,the thesis studies the fractional8)point boundary value problem on infinite interval.Derivative terms of the function1)(,??,₀₊??)and8)point boundary value condition are the difficulties in studying positive solutions of such boundary value problem.In this chapter,the thesis mainly constructs suitable?69?(6(8?space and Cone,adopts different assumptions,and proves that the system has unique solution by using the fixed point theorem of a sum operator and proves the system has at least one solution by using the(8?(6?90?fixed point theorem.In the fourth chapter,the thesis studies a class of fractional boundary value problem with parameters on infinite interval.The difficulty of studying the solution of this kind of boundary value problem is the wide range and the boundary conditions with parameters,and the key to study the positive solution of the boundary value problem is to determine the constraint conditions of the parameters.In this chapter,the thesis proves that there exists at least one solution and a unique solution for the system by using Cone compression and Cone expansion fixed point theorem and the Compressed image principle.In the fifth chapter,the thesis summarizes the main contents and conclusions of this article,and proposes the future research on the boundary value problems of fractional differential equations on infinite interval.