The Existence Of Solutions For Fractional Differential Equations With Integral And Infinite-point Boundary Conditions

Fractional order differential equation is the research direction with great theoretical significance and wide practical application in modern mathematics.The study of fractional order differential equation at first only exist in the pure theoretical study,In recent decades,the research achievements of fractional differential equation has been used more and more in optics and thermal systems,computational mathematics,economics,mathematics,power system,information processing and system identification,and other fields.In numerous subjects of the fractional order differential equations of fracti-onal differential equation with boundary conditions of study is more attention by many scholars,including the nonlinear boundary conditions and coupling system problems and infinitely more.Fractional order differential equations in the coupling system of research is just developed in recent years,it has strong applicability in various fields,so it's in the study of the fractional integral equation is meaningful,in is also an integral part of fractional integral equation of the developing.The existence of solutions for fractional differential equations with integral and infinite multipoint boundary conditions is studied in this paper.In this stu dy,different methods were used,mainly using Leray-Schauder degree theory,Leray-Schauder nonlinear alternative,Banach contracting mapping principle,Kranosel 'skill fixed point theory.The organizational structure of this paper is as follows:In the first chapter,we introduces the historical background and research significance of the problems studied in this paper and the basic concepts and lemmas.In the second chapter,we use Leray-Schauder degree theory,Leray-Schauder nonlinear alternative,to study the boundary value problem of a class of nonlinear fractional order with R-S integral boundary conditions,and obtain several new existence results.Finally,an example is given to prove the applicability of the main conclusion.In the third chapter,a class of fractional order differential equation with nonlinear integral boundary value conditions is studied,and the existence of the maximum minimum solution of the boundary value problem is obtained by using the monotone iterative technique and the method of upper and lower solution.In the fourth chapter,we study the positive solutions of the boundary con-dition coupled system with infinite points,and study it's variant:the positive solution of the coupled system with an infinite number of integral conditions.