Homotopy perturbation method for nonlinear oscillators with coordinate-dependent mass

The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators

“…Nonlinear oscillations arise everywhere in our everyday life and engineering. As an exact solution might be too complex to be used for a practical application, many analytical methods have been used in open literature, for example, the variational iteration method, [1][2][3][4][5][6][7] the homotopy perturbation method, [8][9][10][11][12][13][14][15][16][17][18][19][20] He-Laplace method, [21][22][23] the variational approach [24][25][26][27][28][29] and the Hamiltonian approach. 30,31 The most important property of a nonlinear oscillator is the relationship between the frequency and its amplitude, the simplest method to estimate the frequency-amplitude relationship might be He's frequency formulation [32][33][34] and the max-min approach, 35,36 which are still under development and many modifications were proposed to improve the accuracy.…”

Vibration of an axially moving jet in a dry spinning process

“…This paper is a preliminary study for the string-like vibration of a moving jet. A more sophisticated model is needed to exactly study the jet vibration, and the nonlinear system has to be solved by the homotopy perturbation method, [23][24][25][26] and the frequency-amplitude relation becomes much more complex than that discussed in literature. 27 This is a preliminary theoretical analysis on the effect of vibration on the spinning process.…”

On the solution of time‐fractional dynamical model of Brusselator reaction‐diffusion system arising in chemical reactions

“…Some essential investigation on FC has been analyzed in the past few years, and different books have been published by many authors such as Baleanu et al, 9 Miller and Ross, 10 Kilbas et al, 11 and Podlubny. 12 Several approximate and analytical techniques have been established for such type of problems (see other studies [13][14][15][16][17][18][19][20][21][22][23][24][25][26] ).…”