Upper And Lower Solutions For Boundary Value Problems Of Fractional Differential Equations

In this paper,we study the upper and lower solutions of boundary value problems for fractional order nonlinear differential equations by using the iterative method,fixed point theorem and cone theory of nonlinear functional analysis.This paper is divided into four chapters.In Chapter 1,we introduce the research background and main research contents.In Chapter 2,Firstly,we introduce some concepts and theorems to be used in this paper.including Riemann-Liouville fractional differential and integral definition,the fixed point theorems and Arzela-Ascoli theorem.In Chapter 3,We mainly use the existence of maximal and minimal solutions of boundary value problems of the upper and lower solution method and monotone iterative reconciliation,understand the process,finally we give some examples to illustrate the application of theorem.In Chapter 4,We mainly consider the boundary value problem of nonlinear fractional equation Existence of positive solutions,where 3<?<4is a real number,cD0+? +is the order Caputo fractional derivative.