Existence of Positive Solutions of Three-point Boundary Value Problem for Higher Order Nonlinear Fractional Differential Equations

作     者：韩仁基 葛建生 蒋威 

作者机构：Department of Basic CoursesHuishang Vocational College School of Mathematical SciencesAnhui University 

出 版 物：《Chinese Quarterly Journal of Mathematics》 (数学季刊（英文版）)

年 卷 期：2012年第27卷第4期

页      面：516-525页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the National Nature Science Foundation of China(11071001) Supported by the Key Program of Ministry of Education of China(205068) 

主　　题：nonlinear fractional differential equation three-point boundary value problem positive solutions green’s function banach contraction mapping fixed point theorem in cones 

摘      要：In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α＋u（t）＋f（t,u（t）,u＇（t）,…,u^（n-3）（5）,u^（n-2）（t））=0,u^（i）（0）=0,0≤i≤n-2,u^（n-2）（1）-βu^（n-2）（ξ）=0,where 0〈t〈1,n-1〈α≤n,n≥2,ξ Е（0,1）,βξ^a-n〈1. We first transform it into another equivalent boundary value problem. Then, we derive the Green＇s function for the equivalent boundary value problem and show that it satisfies certain properties. At last, by using some fixed-point theorems, we obtain the existence of positive solution for this problem. Example is given to illustrate the effectiveness of our result.