一类非线性混合分数阶微分方程系统解的稳定性  

The stability of solutions for a class of nonlinear mixed fractional differential equations

作　　者：葛月英 葛琦[1] GE Yueying;GE Qi(College of Science,Yanbian University,Yanji 133002,China)

机构地区：[1]延边大学理学院,吉林延吉133002

出　　处：《延边大学学报（自然科学版）》2024年第1期1-12,共12页Journal of Yanbian University（Natural Science Edition）

基　　金：吉林省教育厅科学技术研究项目(JJKH2022527KJ);吉林省科技厅项目(2023010129JC)

摘　　要：研究了一类含Caputo型非线性混合分数阶微分方程耦合系统的边值问题,首先,利用Banach压缩映射原理讨论了该系统解的存在唯一性,并利用Dhage不动点定理研究了该系统解的存在性;然后,研究了该系统解的Ulam-Hyers稳定性、G-Ulam-Hyers稳定性和Ulam-Hyers-Rassia稳定性,并利用算例验证了所得结果的正确性.The boundary value problem of a class of coupled systems with Caputo type nonlinear mixed fractional differential equations was studied.Firstly,the existence and uniqueness of system solutions were discussed by Banach compression mapping principle,and the existence of system solutions is studied by Dhage fixed point theorem.Then,the Ulam-Hyers stability,G-Ulam-Hyers stability and Ulam-Hyers-Rassia stability of the system solutions were investigated,and the correctness of the obtained results it was verified by numerical examples.

关 键 词：分数阶微分方程 BANACH压缩映射原理 Dhage不动点定理 稳定性 

分 类 号：O175.6[理学—数学]