Existence Of Solutions For Several Types Of Fractional Differential Equations With Boundary Value Problems

In recent years,the theory of fractional calculus is widely used in many fields,and the existence of solutions is the basis to study the progressive stability of solutions.Therefore,it is of great significance to study the existence and uniqueness of solutions of boundary value problems of fractional differential equations.This thesis mainly studies the existence and uniqueness of solutions of five kinds of fractional differential equation boundary value problems by using fixed point theorem,topological degree theory and compression mapping principle.The whole dissertation is divided into four chapters,as follows:In chapter 1:The research background,research status,main work and some basic knowledge are introduced from four aspects of p-Laplacian operator,impulsive differential equations,Hadamard type fractional differential equations and coupled systems.In chapter 2:We study the existence of solutions for two kinds of boundary value problems of Caputo type fractional differential equations with p-Laplacian operators.Firstly,the Schauder fixed point theorem is used to discuss the existence of solutions of a class of fractional differential equations with p-Laplacian operators and integral boundary value conditions.Secondly,the Schauder and Leray-Schauder fixed point theorems are used to study the existence of solutions of a class of boundary value problems of fractional differential equations with p-Laplacian operators and impulse terms.Our results have extended some of the existing conclusions.In chapter 3:We study the existence and uniqueness of solutions for two kinds of boundary value problems of Hadamard type fractional differential equations.Firstly,by using the Leray-Schauder alternative theorem and the compression mapping principle,the sufficient conditions for the existence and uniqueness of solutions of a class of Hilfer-Hadamard type three-point boundary value problems are established respectively.Secondly,by applying Krasnosel’skii fixed point theorem and Banach fixed point theorem,sufficient conditions are obtained for the existence and uniqueness of solutions for a class of Caputo-Hadamard type two-point boundary value problems for fractional differential equations.Our results have extended some of the existing conclusions.In chapter 4:Using the theory of topological degree,the existence result of the boundary value problem of a class of fractional differential equation coupled system with integral boundary value condition is obtained.The results are entirely new.