Homotopy Perturbation Method for the Fractal Toda Oscillator

被引：126
作者：
He, Ji-Huan [1 ,2 ,3 ]
El-Dib, Yusry O. [4 ]
Mady, Amal A. [4 ]
机构：
[1] Xian Univ Architecture & Technol, Sch Sci, Xian 710055, Peoples R China
[2] Henan Polytech Univ, Sch Math & Informat Sci, Jiaozuo 454003, Henan, Peoples R China
[3] Soochow Univ, Coll Text & Clothing Engn, Natl Engn Lab Modern Silk, 199 Ren Ai Rd, Suzhou 215123, Peoples R China
[4] Ain Shams Univ, Fac Educ, Dept Math, Cairo 11517, Egypt
来源：
FRACTAL AND FRACTIONAL | 2021年 / 5卷 / 03期
关键词：
fractal Hamilton principle; fractal Weierstrass theorem; strong minimum condition; Toda oscillator homotopy perturbation method; frequency-amplitude relationship; RANK UPGRADING TECHNIQUE; VARIATIONAL PRINCIPLE;
D O I：
10.3390/fractalfract5030093
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页数：8
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