一类非线性分数阶四点边值问题解的存在性和唯一性  

Existence and Uniqueness of Solutions for a Class of Nonlinear Fractional Four Point Boundary Value Problems

作　　者：郝晓红 程智龙 HAO Xiao-hong;CHENG Zhi-long(WenZheng College of Soochow University,Suzhou 215104,China;School of Mathematics and Physics,Suzhou University of Science and Technology,Suhzou 215009,China)

机构地区：[1]苏州大学文正学院,江苏苏州215104 [2]苏州科技大学数理学院,江苏苏州215009

出　　处：《数学的实践与认识》2018年第16期297-302,共6页Mathematics in Practice and Theory

基　　金：安徽省自然科学基金(KJ2016A071);质量工程项目(2016xjjyxm04)

摘　　要：应用Leray-Schauder非线性抉择定理和Banach压缩映像原理,讨论一类非线性分数阶微分方程四点分数阶边值问题D0α＋u（t）=f（t,u（t））,0〈t〈1,3〈α≤4,I0^4-αu（0）=0,D0＋α-1u（0）＋αD0＋α-1u（ζ）=0,D0＋α-2u（1）＋bD0＋α-2u（η）=0,D0＋α-3u（0）=0研究了解的存在性与唯一性．并给出例子说明定理的适用性．This paper is concerned with the existence and uniqueness of solutions for a class of nonlinear fractional differential equations with four point fractional boundary value conditions D0α＋u（t）=f（t,u（t））,0〈t〈1,3〈α≤4,I0^4-αu（0）=0,D0＋α-1u（0）＋αD0＋α-1u（ζ）=0,D0＋α-2u（1）＋bD0＋α-2u（η）=0,D0＋α-3u（0）=0 By applying Leray-Schauder nonlinear alternative theorem and Banach contraction principle. Examples are presented to illustrate our results.

关 键 词：分数阶微分方程 边值问题 非线性抉择定理 存在唯一性 

分 类 号：O175.8[理学—数学]