A powerful and simple frequency formula to nonlinear fractal oscillators

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.

Automated summary

In this work, a fractal nonlinear oscillator is established in a fractal space using fractal derivative and its variational principle is obtained. The variational principle provides conservation laws in an energy form, and the approximate frequency of the fractal oscillator is found using a simple fractal frequency formula. An example demonstrates the effectiveness of the fractal frequency formula as a powerful and simple tool for fractal oscillators.