Existence Of Solutions For Fractional Differential Coupled Systems

In recent years,Fractional order differential coupled systems in maths is a high degree of concern and attention.With fractional order differential equations in different discipline engineering fields,the fractional order differential equation model is established,such as signal and image processing,economics,control theory,physics,etc.Fractional differential equations play an increasingly important role in these fields.With the continuous improvement of fractional differential coupled system,the application and development of the theory of calculus,the existence theory of solutions to differential equations has important value and significance.Now there are many mathematics workers for abstracted from the practical problems of fractional differential coupled systems have great interest and some scholars by using topological degree theory research with multi-point boundary value problem of the coupling system of fractional differential equations,the existence and uniqueness of using Krasnoselskii fixed point theory and cone in nonlinear Leray-Schauder choose theorem,the coupled system of nonlinear fractional differential equations of the existence of the solution using the theory of critical point with multiple bounded boundary value conditions of the existence of fractional order differential equation with multiple solutions.As a result,the problem of the existence of the solution of the differential coupled system is getting more and more attention.In this paper,the existence and uniqueness of solutions of fractional differential coupled systems are studied.This article is divided into four chapters.The first chapter is the introduction,introduces the related development of fractional order differential coupled systems,some opinions of predecessors for coupling system and how to use the related theorem proving differential existence and uniqueness of the solution of coupled system,also gives about the definition of fractional order differential coupled systems and lemma.The second chapter studies the existence of solutions of a class of fractional differential coupled systems.In this chapter,the existence and uniqueness of the solution are proved by using the principle of compression image and leray-schauder binary choice.In the third chapter,the existence of positive solutions for multipoint boundary value problems in coupled systems is studied.?With 2 < p,q ? 2,k > 0.In this chapter,the existence and uniqueness of positive solutions for multipoint boundary value problems in coupled systems are studied by applying the knowledge of compression images and agglomeration images.In chapter 4,the existence of solutions of nonlinear coupled systems with multipoint boundary conditions is studied.In this chapter,Liouvill-Caputo fractional differential equation with multipoint boundary value problem is studied,and the existence of solution of fractional differential coupled system is studied by using the principle of compression image.