适型分数阶微分方程解的存在唯一性与稳定性  

Existence,Uniqueness and Stability of Solutions of Conformable Fractional Differential Equation

作　　者：张鲁潮[1] 刘锡平[1] 贾梅[1] 宇振盛[1] ZHANG Luchao;LIU Xiping;JIA Mei;YU Zhensheng(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《吉林大学学报(理学版)》2025年第2期287-296,共10页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12371308;12271362);上海理工大学教师发展研究项目(批准号:CFTD2024ZD12)。

摘　　要：利用Schauder不动点定理和Banach压缩映射原理,研究一类具有时滞的适型分数阶脉冲微分方程边值问题,建立了其解的存在唯一性定理,并基于此得到了Ulam-Hyers稳定性和Ulam-Hyers-Rassias稳定性的结论,最后给出一个实例验证理论结果.By using Schauder fixed point theorem and Banach compression mapping principle,we studied a class of conformable fractiona l impulsive differential equation boundary value problems with delay,and established the existence and uniqueness theorems of the solutions.Based on this,we obtained the conclusions of Ulam-Hyers stability and Ulam-Hyers-Rassias stability.Finally,we provided an example to verify the theoretical results.

关 键 词：适型分数阶导数 脉冲 时滞 存在唯一性 Ulam-Hyers稳定性 Ulam-Hyers-Rassias稳定性 

分 类 号：O175.8[理学—数学]