FIXATION OF THE RELATION BETWEEN FREQUENCY AND AMPLITUDE FOR NONLINEAR OSCILLATOR HAVING FRACTIONAL TERM APPLYING MODIFIED MICKENS’ EXTENDED ITERATION METHOD

Abstract

A modified extended iteration procedure is applied to compute the analytical periodic solutions of the nonlinear oscillator having fractional terms. A nonlinear oscillator with force is given to demonstrate the effectiveness and expediency of the iteration scheme. Mickens’ extended iteration method is a well-established method for studying random oscillations. The method is also simple and straightforward to accomplish approximate frequency and the corresponding periodic solution of the strongly nonlinear oscillator. The method gives high validity for both small and large initial amplitudes of oscillations. We have used an appropriate truncation of the obtained Fourier cosine series in each step of iterations to determine the approximate analytic solution of the oscillators. The second, third, and fourth approximate frequencies of the truly nonlinear oscillator with force show a good agreement with their exact values. Also, we have compared the calculated results with some of the existing results. We have shown that the method performs reasonably better.