Existence Of Solutions Of Fractional Differential Systems With Boundary Conditions On Infinite Interval

The theory of fractional differential equation with boundary value conditions has been widely used in more and more fields,which also makes the study of boundary value prob-lems be widely concerned by many domestic and foreign scholars.At present,there have been many achievements about the fractional differential equation with boundary value conditions.This thesis mainly discusses the existence of solutions for boundary value problems of two kinds of Riemann-Liouville fractional differential systems,by using Krasnoselskii fixed point theorem and the extension of Mawhin's continuation theorem.This thesis is divided into four chapters,and the specific contents are following:Chapter 1 is the introduction part,which mainly introduces the research background,the research status,the main work of this thesis and the basic concepts and properties of some fractional calculus.In chapter 2,we study a class of fractional differential system with integral boundary conditions on infinite interval.By analyzing the properties of Green function,we define the space and operator,with the aid of Krasnoselskii fixed point theorem,and prove that the boundary value problem has at least one positive solution.Moreover,an example is given to illustrate the main results.In chapter 3,we are concerned with a class of fractional differential system with p-Laplacian operator based on multi-point boundary value conditions at resonance on infinite interval.By constructing the quasi-linear operator and using the extension of Mawhin's continuation theorem,this chapter shows the boundary value problem has at least one solution.Moreover,an example is given to illustrate the main results.Chapter 4 summarizes the main results of this thesis and prospects for future research.