HOMOTOPY PERTURBATION METHOD FOR FRACTAL DUFFING OSCILLATOR WITH ARBITRARY CONDITIONS
Ji‐Huan He, Man-Li Jiao, Chun‐Hui He
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.
Topics & Concepts
Duffing equationFractalHomotopy perturbation methodNonlinear systemMathematicsMathematical analysisHomotopy analysis methodPerturbation (astronomy)HomotopyVibrationPhysicsPure mathematicsAcousticsQuantum mechanicsFractional Differential Equations SolutionsAdvanced Mathematical Theories and ApplicationsIterative Methods for Nonlinear Equations