分数阶微分包含三点边值问题解的Filippov型存在性定理  

A Filippov’S Theorem on Existence of Solutions for Fractional Differential Inclusions with Three-Point Boundary Value Conditions

作　　者：杨丹丹[1,2] YANG Dan-dan(School of Mathematical Science,Huaiyin Normal University,Huaian 223300,China;Department of Mathematics,The University of Iowa,Iowa city,Iowa State 52240,USA)

机构地区：[1]淮阴师范学院数学科学学院 [2]爱荷华大学数学系

出　　处：《数学的实践与认识》2018年第21期163-170,共8页Mathematics in Practice and Theory

基　　金：江苏省高校优秀中青年教师和校长境外研修项目;江苏省自然科学基金(BK20151288);国家自然科学基金(11701206)

摘　　要：分数阶微分方程是整数阶微分方程的推广,近年来受到广泛关注.2011年,Wang、Tisdell、Zhang研究了一类带有三点边值条件的分数阶微分方程正解的存在性.本文中,利用多值映射的不动点定理,给出了以下分数阶微分包含三点边值问题解的Filippov型存在性定理：{cD0^α＋y（t）∈F（t,y（t））,t∈（0,1）,α∈（2,3],y（0）=y＂（0）=0,βy（η）=y（1）目的是弥补现有的Filippov型定理研究结果的不足并将已有的单值结果推广到多值情形.Differential equations with fractional order are the generalization of differential equations with integer order, which have been got much attention by mathematicians in recent years. In 2011, Wang, Tisdell and Zhang investigated the existence of positive solutions for a class of fractional differential equations. In this paper, based on fixed-point theorem for multivalue maps, we are concerned with the following fractional order differential inclusions with three-point boundary value Problems：{cD0^α＋y（t）∈F（t,y（t））,t∈（0,1）,α∈（2,3],y（0）=y＂（0）=0,βy（η）=y（1） The Filippove theorem on the existence of solutions for the problem is given. The aim of this paper is to fill the gap that there are few results about Filippov theorem and extend known single value result to multi-valued framework.

关 键 词：分数阶微分包含 边值条件 Filippov定理 多值映射 

分 类 号：O175[理学—数学]