分数阶时滞微分方程的Hyers-Ulam稳定性  

Hyers-Ulam Stability of a Class of Fractional Delay Differential Equations

作　　者：顾鹏飞 李刚[1] 刘莉 

机构地区：[1]扬州大学,数学科学学院,江苏 扬州

出　　处：《应用数学进展》2022年第3期1464-1473,共10页Advances in Applied Mathematics

摘　　要：本文研究的是一类半线性分数阶时滞微分方程的Hyers-Ulam稳定性问题。我们根据微分方程的解与逼近方程的解在初始区间所满足的条件是否一致,将问题分成两种情形进行讨论。我们采用了逐次逼近、不动点理论、Gronwall型不等式等方法。最后我们分别得到了这两种情况下分数阶时滞微分方程的Hyers-Ulam稳定常数。In this paper, we devoted to study the Hyers-Ulam stability problem of a class of semilinear fractional delay differential equations. We divide this problem into two cases according to whether the initial conditions of the exact solution and the approximate solution of the differential equation are consistent. We use the successive approximation method, Weissinger’s fixed point theorem and Gronwall’s inequality. Finally, we prove the fractional delay differential equations are Hyers-Ulam stable and obtain two Hyers-Ulam stability constants in the two cases, respectively.

关 键 词：HYERS-ULAM稳定性 有限时滞 分数阶微分方程 GRONWALL不等式 

分 类 号：O175[理学—数学]