状态依赖时滞Caputo分数阶泛函微分方程的可解性  

On Caputo Fractional Functional Differential Equations with State-dependent Delay

作　　者：许文莉 王奇[1] XU Wenli;WANG Qi(School of Mathematical Sciences,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学数学科学学院,安徽合肥230601

出　　处：《滨州学院学报》2023年第4期52-55,共4页Journal of Binzhou University

基　　金：安徽省教育厅自然科学基金重点项目(KJ2018A0027)。

摘　　要：考虑状态依赖时滞Caputo分数阶泛函微分方程解的存在唯一性。首先利用Schaefer不动点定理及Gronwall不等式得到方程解的存在性;然后利用适用于分数阶微积分的广义Winston单调滞后条件得到解的唯一性,推广了已有的结果。The existence and uniqueness of solutions for Caputo fractional functional differential equations with state-dependent delay is considered.The existence of the solution is obtained by using Schaefer fixed point theorem and Gronwall inequality,then the uniqueness of the solution is obtained by using the generalized Winston monotone lag condition that is suitable for fractional differential equation,which extends the existing results.

关 键 词：状态依赖时滞 Caputo分数阶泛函微分方程 Schaefer不动点定理 Gronwal不等式 广义Winston单调滞后条件 

分 类 号：O175.12[理学—数学]