When an oscillator vibrates in a porous medium or along an unsmooth surface, a fractal model can be adopted using the two-scale fractal derivative. This paper elucidates a simple but effective method for fast and exclusive insight into the asymptotically periodic property at the initial stage and the extremely low frequency property when time tends to infinity. Some examples are illustrated to show the one-step solution process and the accurate results.
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He et al. (2021) studied this question.
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