论文标题
从谐波振荡器阻尼因子确定分数衍生级阶
Fractional derivative order determination from harmonic oscillator damping factor
论文作者
论文摘要
本文分析代表阻尼和分数振荡器的微分方程。首先，表明在分数演算中使用物理量之前，必须将它们变为无量纲。之后，将两个方程参数相关的近似表达式显示了分数订单接近整数编号的情况。随后，使用功率序列扩展进行数值回归，并且从分数计算中，两个方程都不能等效。最后，从数值回归数据中，将两个方程参数的分析近似表达式进行了完善。
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless. Afterwards, approximated expressions that relate the two equations parameters for the case that the fractional order is close to an integer number are presented. Following, a numerical regression is made using power series expansion, and, also from fractional calculus, the fact that both equations cannot be equivalent is concluded. In the end, from the numerical regression data, the analytical approximated expressions that relate the two equations' parameters are refined.
