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...
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| Published in | Fractal and fractional Vol. 5; no. 3; p. 93 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Basel
MDPI AG
2021
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| Subjects | |
| Online Access | Get full text |
| ISSN | 2504-3110 2504-3110 |
| DOI | 10.3390/fractalfract5030093 |
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| Abstract | 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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| AbstractList | 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. |
| Author | He, Ji-Huan Mady, Amal A. El-Dib, Yusry O. |
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| Snippet | The fractal Toda oscillator with an exponentially nonlinear term is extremely difficult to solve; Elias-Zuniga et al. (2020) suggested the equivalent... |
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| SubjectTerms | 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 |
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| Title | Homotopy Perturbation Method for the Fractal Toda Oscillator |
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