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
DOI: 10.12677/AAM.2022.113160, PDF,    国家自然科学基金支持
作者: 顾鹏飞, 李 刚*, 刘 莉：扬州大学，数学科学学院，江苏 扬州
关键词: Hyers-Ulam稳定性；有限时滞；分数阶微分方程；Gronwall不等式；Hyers-Ulam Stability； Finite Delay； Fractional Differential Equations； Gronwall’s Inequality
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。
Abstract: 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.
文章引用：顾鹏飞, 李刚, 刘莉. 分数阶时滞微分方程的Hyers-Ulam稳定性[J]. 应用数学进展, 2022, 11(3): 1464-1473. https://doi.org/10.12677/AAM.2022.113160

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