Existence Of Positive Solutions For Boundary Value Problems Of Fractional Differential Equations On Infinite Interval

In this paper,we study the boundary value problems of fractional differential equations on infinite interval.Three classes of differential equations with Riemann-Liouville fractional derivative are studied.By constructing suitable Banach space and using fixed point theorems,the existence,multiplicity and nonexistence of positive solutions for boundary value problems on infinite intervals are obtained.The main work of this paper is divided into six parts.In Chapter one,the research background and research status of fractional order differential equations are summarized.We mainly introduce the results of the scholars in the field of fractional differential equations,which leads to the main content of this paper.In Chapter two,we introduce the basic concepts of fractional differential and integral,we also give some lemma and basic theory which will be used in the following study.In Chapter three,we study the existence of positive solutions for a class of fractional differential equations on the infinite interval with the integral boundary conditions.In this chapter,we establish the equivalent integral equations of the original differential equations and get the Green function,moreover,we discuss the properties of the Green function.Then by using Krasnoselskii fixed point theorem,we obtain the existence results of positive solutions for the boundary value problem with ? in different cases.At the last,we also give two corollaries.In Chapter four,we consider a class of fractional differential equations with integral boundary conditions which involve two disturbance parameters.By constructing suitable Banach space and special cone,and using cone expansion and cone compression fixed point theorem,the existence and nonexistence of positive solutions for the boundary value problem in infinite interval are obtained.In Chapter five,we consider a class of infinite-points boundary value problems of fractional differential equations on the half-line with a disturbance parameter.By using the method of upper and lower solutions,fixed point index theory and some fixed point theorems,the existence,multiplicity and nonexistence of the positive solution of the boundary value problem are obtained,respectively.The impact of the disturbanceparameters on the existence of positive solutions is also given.In Chapter six,we summarize the main research contents and achievements of this article.