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在Power Caputo分数运算符及其对称案例下,具有冲动效应的机械振荡器方程的解决方法行为
Hicham Saber1, Mohammed Almalahi2,3, Mohamed Bouye4
1Department of Mathematics, College of Science, University of Ha'il, Ha'il, 55473, Saudi Arabia.
Scientific reports
|May 9, 2025
概括
本研究引入了一个灵活的分数运算符来分析具有记忆和冲动效应的机械振荡器. 它严格证明了解决方案的存在,独特性和稳定性,增强了系统建模.
科学领域:
- 分数微积分的计算.
- 非线性动力学是一种非线性动力学.
- 应用数学 应用数学 应用数学
背景情况:
- 机械振荡器经常表现出复杂的行为,包括记忆效应和突然的冲动.
- 现有的分数运算符可能缺乏灵活性来准确地捕捉这些组合现象.
- 一般化的分数运算符为更全面的建模提供了一个有希望的途径.
研究的目的:
- 为了研究具有冲动效应的机械振荡器的定性行为,使用一种新的通用分数运算符.
- 为解决方案的存在,独特性和Ulam-Hyers稳定性建立条件.
- 开发一个数值方案来近似解决方案.
主要方法:
- 使用一个通用的Power Caputo分数运算符,参数为'p'用于灵活的内存建模.
- 使用积分方程公式和固定点理论 (巴纳赫的收缩原理).
- 开发基于拉格朗日插值多项式的数值方案.
主要成果:
- 为解决方案的存在,独特性和Ulam-Hyers稳定性建立了严格的条件.
- 一般化运算符包括已知的分数导数,如卡普托-法布里齐奥和阿坦加纳-巴莱努.
- 成功开发了一种用于近似解决方案的数值方法.
结论:
- 拟议的概括分数运算符为模型机械振荡器提供了一个强大的框架,它既具有分数内存,也具有冲动动态.
- 该研究提供了增强的数学严谨性和数值工具,以提高工程和控制系统的准确性.
- 这种方法有助于理解和模拟复杂的动态系统.
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