中立型Caputo分数阶泛函微分方程解的存在性和Hyers-Ulam稳定性  

Existence and Hyers-Ulam Stability of Neutral Caputo Fractional Functional Differential Equations

作　　者：王奇[1] 邓茜茜 解晨曦 胡玉婷 WANG Qi;DENG Qianqian;XIE Chenxi;HU Yuting(School of Mathematical Sciences,Anhui University,Hefei 230601,China;School of Big Date and Statistics,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 [2]安徽大学大数据与统计学院,安徽合肥230601

出　　处：《山东航空学院学报》2024年第4期139-144,共6页Journal of Binzhou University

基　　金：安徽省教育厅自然科学基金重点项目(KJ2018A0027);安徽大学大学生创新训练项目(X202310357005)。

摘　　要：考虑具有无穷时滞和多个Caputo分数阶导数的中立型分数阶泛函微分方程解的存在性和Hyers-Ulam稳定性。利用压缩映射原理及无穷时滞的相空间理论得到方程解的存在性,并利用分数阶微积分的广义Gronwal型不等式及分数阶积分算子的单调性得到解的Hyers-Ulam稳定性。The existence and Hyers-Ulam stability of neutral fractional functional differential equation with infinite delay and multiple Caputo fractional derivatives are studied.Firstly,the existence of solutions is obtained by using the contraction mapping principle and the phase space theory on infinite delay.Then the Hyers-Ulam stability of solution is obtained by using the generalized Gronwall inequality and the monotonicity of the fractional integral operator.

关 键 词：Caputo分数阶泛函微分方程 压缩映射原理 GRONWALL不等式 HYERS-ULAM稳定性 

分 类 号：O175[理学—数学]