The fractional calculus is useful to model nonlocal phenomena. We construct a method to evaluate the fractional Caputo derivative by means of a simple explicit quadratic segmentary interpolation. This method yields to numerical resolution of ordinary fractional differential equations. Due to the nonlocality of the fractional derivative, we may establish an equivalence between fractional oscillators and ordinary oscillators with a dissipative term.

中文翻译：

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具有分数导数的一维系统的近似解

分数阶微积分对于模拟非局部现象很有用。我们构建了一种通过简单的显式二次分段插值来评估分数 Caputo 导数的方法。该方法产生普通分数微分方程的数值分辨率。由于分数导数的非定域性，我们可以在分数振子和具有耗散项的普通振子之间建立等价。