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

As the application of fractional calculus expands gradually,great progress has been made in development of differential equations,some researches related to integer order differential equations boundary value problems have been gradually extended to the researches of fractional order differential equations.The main work of this thesis is to explore the existence of solutions and its multiple positive solutions of several kinds of fractional order boundary value problems of differential equations.The thesis consists of five chapters.Chapter 1 mainly makes introduces the research background and domestic and foreign development of the subject,as well as the relevant definitions and the basic theories to be used in this research.Chapter 2 using the fixed point theorem of Guo-Krasnosellskii's cone stretching and cone contraction,the following fractional differential equations with integral boundary value conditions are studied under the definition of conformable fractional derivative,(?)(2.1)the existence of solutions and its multiple positive solutions are given.and one example is given.Chapter 3 using Leray-Schauder degree theory,discusses and obtained the following boundary value problem of fractional differential equations,(?)(3.1)the existence of multiple positive solutions under the definition of conformable fractional derivative,and two concrete examples are given.Chapter 4 using Schaefer fixed point theorem,discusses the existence of the solutions boundary value problem of fractional differential equations,(?)(4.1)get the knowledge of the existence theorem,and finally give examples to verify the conclusion.Chapter 5 is a summary of the thesis and prospect for future research.