一类非线性Caputo型分数阶微分方程耦合系统的正解  

Positive Solutions of a Coupled System of Nonlinear Caputo Type Fractional Differential Equations

作　　者：薛益民[1] 苏莹[1] 苏有慧[1] XUE Yimin SU Ying SU Youhui(School of Mathematics and Physical Science, Xuzhou Institute of Technology , Xuzhou 221018, Jiang su Province, China)

机构地区：[1]徐州工程学院数学与物理科学学院,江苏徐州221018

出　　处：《吉林大学学报（理学版）》2017年第4期853-860,共8页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11301454);国家自然科学基金数学天元基金(批准号:11526177);江苏省自然科学基金(批准号:BK20151160);江苏省高校自然科学基金(批准号:14KJB110025);江苏省六大人才高峰项目(批准号:2013-JY-003);安徽省教育厅重点项目(批准号:KJ2017A839)

摘　　要：利用Schauder不动点定理、Leray-Schauder抉择理论和Banach不动点定理,研究一类含积分边值条件的非线性Caputo型分数阶微分方程耦合系统边值问题,得到了该耦合系统正解存在性和唯一性的充分条件,并举例说明定理的适用性.We studied the boundary value problem of a coupled system of a class of nonlinear Caputo type fractional differential equations with integral boundary value conditions by applying Schauder fixed point theorem,Leray-Schauder choice theory and Banach fixed point theorem.We obtained sufficient conditions for the existence and uniqueness of positive solutions of the coupled system,and illustrated the applicability of the theorem by examples.

关 键 词：分数阶微分方程 耦合系统 正解 不动点定理 

分 类 号：O175.8[理学—数学]