An improved homotopy perturbation method for solving local fractional nonlinear oscillators

Abstract

Local fractional nonlinear oscillators are studied by a modification of the homotopy perturbation method coupled with the variational iteration method. In the solution process, the fractional variational iteration method is adopted to transform the nonlinear oscillator equation into an integral equation, which is then decomposed into a series of equations, which are solved by the homotopy perturbation method. Two examples are given to show that the proposed method is simpler and more flexible than the classical homotopy perturbation method. It is also shown that the key to use this method is to select the appropriate decomposition of the initial value series.