Abstract
The challenge for a non-linear vibration system in a fractal space is more fractal dimensions than frequency-amplitude relationship, the system energy consumption depends upon its fractal property, so its best-case scenario is to establish a relationship among the fractal dimensions, frequency and amplitude. For this purpose, this paper studies a fractal-fractional vibration system of a mass attached to a stretched elastic wire in a fractal space, and its asymptotic periodic property is elucidated, the effect of the fractal dimensions on the vibration system is discussed. This paper offers a new road to fast and reliable analysis of fractal oscillators with high accuracy.
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