Abstract
In this work, a fractal nonlinear oscillator is successfully established by fractal derivative in a fractal space, and its variational principle is obtained by semi-inverse transform method. The variational principle can provide conservation laws in an energy form. The approximate frequency of the fractal oscillator is found by a simple fractal frequency formula. An example shows the fractal frequency formula is a powerful and simple tool to fractal oscillators.
Highlights
The oscillator is a very common phenomenon in nature such as the oscillator of the springs, the oscillator of water waves, and so on. These oscillator phenomena can be described by the oscillator equation.[1,2,3,4]
The general oscillator equation is established in a continuous space
We find He’s frequency formula is valid for fractal nonlinear oscillator with He’s fractal derivative
Summary
The oscillator is a very common phenomenon in nature such as the oscillator of the springs, the oscillator of water waves, and so on. These oscillator phenomena can be described by the oscillator equation.[1,2,3,4] The general oscillator equation is given as follows d2v dt[2] þ fðvÞ The general oscillator equation is established in a continuous space. Equation (1) can be described by He’s fractal derivative as follows
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