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具有状态依赖时滞的Caputo分数阶中立型泛函微分方程的柯西问题
On the Cauchy Problem of Caputo Fractional Functional Differential Equations of Neutral Type with State-dependent Delay
【摘要】 具有状态依赖时滞的泛函微分方程是微分系统的重要内容。文章研究具有状态依赖时滞的Caputo分数阶中立型泛函微分方程的柯西问题。先利用Schaefer不动点定理及Gronwall不等式技巧得到该方程解的存在性,然后利用广义Winston单调时滞条件和反证法得到该方程解的唯一性结论,推广已有的结果。
【Abstract】 Functional differential equations with state-dependent delays is an important content of differential systems. A class of Caputo fractional functional differential equations of neutral type with state-dependent delay is studied. The existence of solution for this equation is first obtained by using Schaefer fixed point theorem and Gronwall inequality technique,then the uniqueness results of solution is obtained by using the generalized Winston monotone lag condition and reduction to absurdity,which extend the existing results.
【关键词】 状态依赖时滞;
Caputo分数阶中立型泛函微分方程;
Schaefer不动点定理;
Gronwall不等式;
广义Winston单调时滞条件;
【Key words】 state-dependent delay; Caputo fractional functional differential equations of neutral type; Schaefer fixed point theorem; Gronwall inequality; generalized Winston monotone lag condition;
【Key words】 state-dependent delay; Caputo fractional functional differential equations of neutral type; Schaefer fixed point theorem; Gronwall inequality; generalized Winston monotone lag condition;
【基金】 安徽省教育厅自然科学基金重点项目(KJ2018A0027)
- 【文献出处】 淮北师范大学学报(自然科学版) ,Journal of Huaibei Normal University(Natural Sciences) , 编辑部邮箱 ,2023年03期
- 【分类号】O175
- 【下载频次】7