Immediate solution for fractional nonlinear oscillators using the equivalent linearized method

Abstract

The existence of the derivative with a fractional-order in a class of differential equations could lead to complicating the analysis. In this paper, a novel approach has been introduced to facilitate the analysis of the oscillation having fractional-order derivatives and to obtain the analytical solution easily. The present technique is formulated to provide an easy way of understanding. The suggested technique has been utilized to study two examples for illustration. The similitude between the analytical and numerical solution verifies and gives satisfactory precision to the equivalent solution. The new technique is represented to be the best tool for solving the nonlinear oscillation problems in physics and engineering which have a fractional-order.