对于没有和具有比例延迟的卡普托-哈达马德型分数微分系统的有限时间稳定性
1School of Mathematics, Hefei University of Technology, Hefei, Anhui 230601, China.
Chaos (Woodbury, N.Y.)
|January 21, 2026
概括
本研究探讨了卡普托-哈达马德类型的分数微分系统 (C-HTFDS) 的有限时间稳定性,无论是有延迟还是没有延迟. 新的方法可以确保系统在有限时间内的性能,这对于实际应用至关重要.
科学领域:
- 分数微积分的计算.
- 动态系统理论 动态系统理论
- 控制理论 控制理论
背景情况:
- 卡普托-哈达马德类型的分数导数是建模超慢动态过程的关键工具.
- 对于实际应用来说,有限时间稳定性是必不可少的,在无限时间范围内提供更好的性能.
- 现有的稳定性分析方法往往不能直接解决带有延迟的分数系统.
研究的目的:
- 调查卡普托-哈达马德类型分数微分系统 (C-HTFDS) 的有限时间稳定性.
- 在两个条件下分析C-HTFDS:没有延迟的系统和带有比例延迟的系统.
- 开发新的分析和数值技术来评估这些系统的有限时间稳定性.
主要方法:
- 对于C-HTFDS的有限时间稳定性标准,使用修改的拉普拉斯变换和自适应的分数格伦沃尔不等式,在没有延迟的情况下建立.
- 新的比例延迟米塔格-莱弗勒矩阵函数是为具有比例延迟的线性C-HTFDS设计的.
- 对于具有比例延迟的非线性C-HTFDS,构建了一个带有两个积分项的比例延迟分数格伦沃尔不等式.
主要成果:
- 建立了对线性和非线性C-HTFDS无延迟的有限时间稳定性标准.
- 开发了使用新的矩阵函数用于具有比例延迟的线性C-HTFDS的基本解决方案.
- 构建并验证了一种具有比例延迟的非线性C-HTFDS的新型分数Gronwall不等式.
- 数字模拟证实了提出的理论发现的有效性.
结论:
- 该研究为分析C-HTFDSs的有限时间稳定性提供了一个全面的框架.
- 开发的方法和不等式对延迟和非延迟的分数系统都有效.
- 这些发现对复杂动态系统的精确控制和表征有重大影响.
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