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Homotopy perturbation Shehu transform method for solving fractional models arising in applied sciences

Maitama Shehu, Zhao Weidong

Journal of Applied Mathematics and Computational Mechanics

2021

Vol. 20, nr 1

71--82

Using the recently proposed homotopy perturbation Shehu transform method (HPSTM), we successfully construct reliable solutions of some important fractional models arising in applied physical sciences. The nonlinear terms are decomposed using He’s polynomials, and the fractional derivative is calculated in the Caputo sense. Using the analytical method, we obtained the exact solution of the fractional diffusion equation, fractional wave equation and the nonlinear fractional gas dynamic equation.

Application of modified homotopy perturbation method to nonlinear oscillations

Marinca V.

Archives of Mechanics

2006

Vol. 58, nr 3

241-256

The purpose of this paper is to apply a version of homotopy technique to nonlinear problems. The modified version of homotopy perturbation method is applied to derive highly accurate analytical expressions for periodic solutions or for approximate formulas of frequency. In contrast with the traditional perturbation methods, the proposed method does not require any small parameter in the equation. The proposed algorithm avoids the complexity provided by other numerical approaches. The analysis is accompanied by three numerical examples. The results prove that this method is very effective and simple.