Approximate analytic solutions for non-linear oscillators with fractional-order restoring force by means of the optimal variational iteration method

Abstract

In this paper, a new approach, namely the optimal variational iteration method (OVIM) was proposed to investigate oscillators with fractional-power nonlinearities. It was illustrated that this approach is very effective and convenient and does not require linearization or small parameter. Unlike other classical iteration methods, only one iteration leads to highly accurate results, due to a rigorous procedure for convergence control. Approximate analytical results obtained through the proposed method were compared with numerical results and an excellent agreement was found, which prove the validity of the proposed procedure. This method can be easily applied to other strongly nonlinear problems. Key words: Optimal variational iteration method, nonlinear differential equation, analytical approximations, fractional-power restoring force.