非线性适型分数阶时滞微分方程初值问题解的存在性分析  

The existence analysis of solutions for initial value problems of nonlinear conformable fractional delayed differential equations

作　　者：王森 蒋威[1] WANG Sen;JIANG Wei(School of Mathematical Sciences,Anhui University,Hefei 230601,Anhui,China)

机构地区：[1]安徽大学数学科学学院,安徽合肥230601

出　　处：《上海师范大学学报（自然科学版）》2021年第3期362-375,共14页Journal of Shanghai Normal University(Natural Sciences)

基　　金：The National Natural Science Foundation of China (11371027)

摘　　要：基于Banach不动点定理、Schauder不动点定理、逐步逼近技巧和适型分数阶积分框架下的Gronwall不等式等方法,建立了适型分数阶导数意义下的非线性分数阶时滞微分方程初值问题解的存在性和唯一性结果.In this paper,we establish several existence and uniqueness results of solutions for initial value problems of nonlinear fractional delayed differential equations in the sense of conformable fractional derivative.The different results of existence of solutions are derived based on Banach fixed point theorem,Schauder fixed point theorem,successive approximations technique and the Gronwall inequality in the frame of conformable fractional integral,respectively.

关 键 词：存在性和唯一性 不动点定理 逐步逼近技巧 GRONWALL不等式 适型分数阶微积分 

分 类 号：O175.1[理学—数学]