The Existence Of Solutions Of Boundary Value Problems For Several Classes Of Fractional Differential Equations

In recent years,as the application background of fractional differential equations gradually expands,great progress has been made in researches of this aspect,and it is widely used in real life,some researches related to integer order boundary value problems have been gradually extended to the researches of fractional order,which has attracted the attention of many scholars.Ordinary differential equations have some limitations when they are used,more and more complex problems in life can not be well interpreted.p-Laplace operator and Langevin differential have been also introduced into such equations and used in many fields.The main work of this thesis is to explore several kinds of fractional order boundary value problems of differential equations.In this thesis,fractional differential equations are mainly studied.The existence of the solution of the boundary value problem are improved and generalized,and the validity of the conclusions is illustrated by concrete examples.The thesis consists of five chapters,the main contents are as follows:In the first chapter,the research history of the subject and the recent development status at home and abroad are introduced,and the basic knowledge needed in this thesis are also introduced.In the second chapter,based on the principle of Banach contractive mapping,the following boundary value problems of the following fractional differential equations is deduced the existence of the solution is given.The uniqueness theorem of the solution and the decision theorem for the existence of one solution at least are obtained,and three examples are given.In the third chapter,by using the fixed point theorem of Guo-Krasnosellskii's,the following boundary value problem of fractional differential equations with p-Laplacian operator is deduced the existence of no positive solution or one positive solution at least is given,and two concrete examples are given.In the fourth chapter,the following boundary value problem of Langevin differential equations with fractional order are discussed the existence of the solution are given,and two concrete examples are given to illustrate the validity of the obtained conclusions.In the fifth chapter,we made a brief summary and prospect for the study in the thesis.