He's frequency formula to fractal undamped Duffing equation

Nonlinear oscillation is an increasingly important and extremely interesting topic in engineering. This article completely reviews a simple method proposed by Ji-Huan He and successfully establishes a fractal undamped Duffing equation through the two-scale fractal derivative in a fractal space. Its variational principle is established, and the two-scale transform method and the fractal frequency formula are adopted to find the approximate frequency of the fractal oscillator. The numerical result shows that He's frequency formula is a unique tool for the fractal equations.

Automated summary

This article discusses the increasing importance of nonlinear oscillation in engineering and introduces a simple method proposed by Ji-Huan He to establish a fractal undamped Duffing equation. The two-scale transform method and the fractal frequency formula are used to find the approximate frequency of the fractal oscillator, showing that He's frequency formula is a unique tool for fractal equations.