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

高阶非线性分数阶微分方程三点边值问题正解的存在性(英文)

作　　者：韩仁基 葛建生 蒋威 

机构地区：[1]Department of Basic Courses,Huishang Vocational College [2]School of Mathematical Sciences,Anhui University

出　　处：《Chinese Quarterly Journal of Mathematics》2012年第4期516-525,共10页数学季刊（英文版）

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

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.

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

分 类 号：O175.8[理学—数学]