Homotopy Analysis Method for a Conservative Nonlinear Oscillator with Fractional Power

Homotopy Analysis Method for Nonlinear Differential Equations with Fractional Orders

Most problems in science and engineering are nonlinear. Thus, it is important to develop efficient methods to solve them. In the past decades, with the fast development of high-quality symbolic computing software, such as Maple, Mathematica and Matlab, analytic as well as numerical techniques for nonlinear differential equations have been developed quickly. The homotopy analysis method (HAM) [1...

Homotopy perturbation method for a conservative x1/3 force nonlinear oscillator

In recent years, considerable attention has been directed towards the study of strongly nonlinear oscillators, and several 2 methods such as perturbation techniques [1–15] or harmonic balance based methods [15–23] have been used to find 3 approximate solutions to nonlinear problems [1–4]. An excellent review of some asymptoticmethods for strongly nonlinear 4 equations can be found in detail in ...

Assessment of Homotopy Analysis Method and Modified Homotopy Perturbation Method for Strongly Nonlinear Oscillator

Some recently developed analytical methods namely; homotopy analysis method, homotopy perturbation method and modified homotopy perturbation method are applied successfully for solving strongly nonlinear oscillators. The analytical results obtained by using HAM are compared with those of HPM, mHPM as well as with numerical results. In this study, different examples with strong nonlinearity are ...

Homotopy analysis method for the fractional nonlinear equations

To find the explicit solutions of nonlinear differential equations, many powerful methods have been used (Abbasbandy, 2006; He, 1998; Wazwaz, 1997; Ghasemi et al., 2007; Adomian and Adomian, 1984). The homotopy analysis method (HAM) (Liao, 2003, 2004; Liao and Tan, 2007; Yamashita et al., 2007) is a general analytic approach to get series solutions of various types of nonlinear equations. The H...

Homotopy Analysis Sumudu Transform Method for Nonlinear Equations