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HOMOTOPY PERTURBATION METHOD FOR FRACTAL DUFFING OSCILLATOR WITH ARBITRARY CONDITIONS

School of Science, Xi’an University of Architecture and Technology, P. R. China

School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, P. R. China

National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, Suzhou, P. R. China

E-mail Address: hejihuan@suda.edu.cn

Corresponding authors.

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MAN-LI JIAO

School of Science, Xi’an University of Architecture and Technology, P. R. China

School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, P. R. China

National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, Suzhou, P. R. China

E-mail Address: jml1290@163.com

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, and

CHUN-HUI HE

School of Science, Xi’an University of Architecture and Technology, P. R. China

School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, P. R. China

National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, Suzhou, P. R. China

E-mail Address: Mathew_He@yahoo.com

Corresponding authors.

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https://doi.org/10.1142/S0218348X22501651Cited by:47 (Source: Crossref)

Abstract

A nonlinear vibration system in a fractal space can be effectively modeled using the fractal derivatives, and the homotopy perturbation method is employed to solve fractal Duffing oscillator with arbitrary initial conditions. A detailed solving process is given, and it can be easily followed for applications to other nonlinear vibration problems.

Keywords:

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