HOMOTOPY PERTURBATION METHOD FOR FRACTAL DUFFING OSCILLATOR WITH ARBITRARY CONDITIONS

Ji-Huan He, Man-Li Jiao and Chun-Hui He
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Ji-Huan He: School of Science, Xi’an University of Architecture and Technology, P. R. China2School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, P. R. China3National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, Suzhou, P. R. China
Man-Li Jiao: School of Science, Xi’an University of Architecture and Technology, P. R. China2School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, P. R. China3National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, Suzhou, P. R. China
Chun-Hui He: School of Science, Xi’an University of Architecture and Technology, P. R. China2School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, P. R. China3National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, Suzhou, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 09, 1-10

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: Fractal-Fractional Derivative; Fractal Spacetime; Discontinuous Problem; Fractal Oscillation; Low Frequency; He’s Frequency Formulation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22501651

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