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

With the rapid development of science and technology,the theory of fractional calculus is widely used in many fields such as material mechanics,control systems,biomedicine and signal processing.In recent years,the research and application of the boundary value problems of fractional differential equations have been widely con-cerned by domestic and foreign scholars.Based on this,the paper mainly studies the existence of solutions for boundary value problems of three types of fractional differen-tial equations,which is divided into five chapters:The first chapter is the introduction,which introduces the research background and the main content of this article,as well as some definitions and theorems of fractional calculus.In the second chapter,we study the existence of positive solution for a class of boundary value problem of Riemann-Liouville fractional differential equations(?)Firstly,the problem can be reduced to the existence problem of fixed points for the in-tegral operator.Then by means of Guo-Krasnoselskii fixed point theorem and Leggett-Williams fixed point theorem,the sufficient conditions for the exsitence of at least one positive solution and three positive solutions for the problem are obtained.We give examples to illustrate the application of the results.In the third chapter,we investigate the existence and uniqueness of solution for a class of boundary value problem of fractional differential equations with integral condi-tions by applying Schauder fixed point theorem and Banach contraction mapping prin-ciple(?).In the fourth chapter,we consider the boundary value problem of a class of Caputo fractional differential equations with a parameter.Some existence results of solutions are obtained by using Leray-Schauder continuation theorem and Banach contraction mapping principle.Finally,two examples are delivered(?).The fifth chapter is the summation,which summarizes the paper and points out the problems that can be studied in the future.