The Study Of Solutions To Fractional Differential Equations

Fractional differential equation is an important branch of differential equation,which is widely used in mathematics,physics,engineering and other fields.It solves the problems of robotics,signal processing and conversion,and becomes one of the important tools of mathematical modeling because of its memorability and genetic characteristics.In order to master and apply this tool better,many scholars began to explore the existence and uniqueness of solutions to fractional boundary value problems.In this paper,the theory of nonlinear functional analysis is used to study fractional differential equations with three classes boundary conditions,and the existence and uniqueness of solutions are obtained.Finally,example are given to prove the feasibility of the results.There are four main chapters in this paper.The first chapter is the introduction,briefly introducing the development process of fractional differential equations and the basic definitions and lemmas that need to be used below.In the second chapter,we consider the coupled system of Caputo fractional differential equations:(?) considering multi-point,Riemann-Stieltjes integral and infinite point boundary value condi-tions respectively:(?)By Schauder fixed point theorem,we get the existence of the system.Finally,in the third chapter,a system of coupled fractional differential equations with three classes boundary conditions is studied(?) the boundary conditions are as follows(?) By improving Lipschitz constant to Lipschitz function,the result is more general,and the uniqueness of solution is obtained by using Banach contraction mapping principle.Finally,the fourth chapter makes a summary of the whole paper.