| 潘仁杰,胡孝澄,凡震彬.非线性Riemann-Liouville型分数阶时滞微分方程解的存在性以及有限时间稳定性[J].数学研究及应用,2024,44(2):225~238 |
| 非线性Riemann-Liouville型分数阶时滞微分方程解的存在性以及有限时间稳定性 |
| Existence and Finite Time Stability of Nonlinear Riemann-Liouville Fractional Delay Differential Equations |
| 投稿时间：2023-03-08 修订日期：2023-11-15 |
| DOI：10.3770/j.issn:2095-2651.2024.02.009 |
| 中文关键词: 分数阶振动微分方程 时滞微分方程 有限时间稳定性 |
| 英文关键词:fractional oscillatory differential equations delay differential equation finite time stability |
| 基金项目:国家自然科学基金(Grant Nos.11871064). |
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| 中文摘要: |
| 本文研究了$\varrho$阶非线性Riemann-Liouville型分数阶时滞振动微分方程解的存在性和有限时间稳定性.我们采用不动点定理来研究解的存在性结果.此外,基于一些重要的不等式,我们研究了系统的有限时间稳定性.最后,通过例子验证了结论的合理性. |
| 英文摘要: |
| This article explores the existence results and finite time stability of nonlinear Riemann-Liouville fractional oscillatory differential equations of order $1<\varrho<2$ with pure delay. The approaches we adopted to explore the existence results are fixed point theorems. What's more, based on some important inequalities, we explore the finite time stability of the system. In the end, the rationality of our conclusion is verified by a case. |
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