分数振荡的扭曲
Twist of fractional oscillations
摘要：
利用拉普拉斯变换的方法，我们考虑分数阶振荡。它们是由普通谐波振动的时钟随机化得到的。与正弦和余弦相反，描述分数振荡的函数表现出有限数量的具有代数衰减的阻尼振荡。导出了它们的分数阶微分方程。
英文摘要：
Using the method of the Laplace transform, we consider fractional oscillations. They are obtained by the time-clock randomization of ordinary harmonic vibrations. In contrast to sine and cosine, the functions describing the fractional oscillations exhibit a finite number of damped oscillations with an algebraic decay. Their fractional differential equation is derived.
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