期刊
FRACTAL AND FRACTIONAL
卷 5, 期 3, 页码 -出版社
MDPI
DOI: 10.3390/fractalfract5030093
关键词
fractal Hamilton principle; fractal Weierstrass theorem; strong minimum condition; Toda oscillator homotopy perturbation method; frequency-amplitude relationship
This paper demonstrates the basic properties of a fractal oscillator using fractal variational theory and introduces a new form of the Toda oscillator free of the exponential nonlinear term through the homotopy perturbation method. The analytical solution is validated through numerical tests, showing excellent agreement, and the graphical illustration further elucidates the effect of the order of the fractal derivative on the vibration property.
The fractal Toda oscillator with an exponentially nonlinear term is extremely difficult to solve; Elias-Zuniga et al. (2020) suggested the equivalent power-form method. In this paper, first, the fractal variational theory is used to show the basic property of the fractal oscillator, and a new form of the Toda oscillator is obtained free of the exponential nonlinear term, which is similar to the form of the Jerk oscillator. The homotopy perturbation method is used to solve the fractal Toda oscillator, and the analytical solution is examined using the numerical solution which shows excellent agreement. Furthermore, the effect of the order of the fractal derivative on the vibration property is elucidated graphically.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据