Homotopy Perturbation Method for the Fractal Toda Oscillator

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 o...

Full description

Saved in:
Bibliographic Details
Published inFractal and fractional Vol. 5; no. 3; p. 93
Main Authors He, Ji-Huan, El-Dib, Yusry O., Mady, Amal A.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 2021
Subjects
Energy
Exact solutions
Fractal analysis
fractal Hamilton principle
fractal Weierstrass theorem
Fractals
frequency-amplitude relationship
Perturbation methods
Software
strong minimum condition
Toda oscillator homotopy perturbation method
Online AccessGet full text
ISSN2504-3110
2504-3110
DOI10.3390/fractalfract5030093

Cover

More Information
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract5030093