The Method of Multiple Time Scales and Finite Differences Method for the van der Pol Oscillator with Small Fractional Damping
Fadime Dal *
Department of Mathematics, Ege University, Izmir, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we consider the van der Pol oscillator with small fractional damping. To construct the approximate and numerical solutions of the equation, the method of multiple time scales and finite differences method are used, respectively. It is shown that the approximate solution is in good agreement with the numerical solution for weakly nonlinear case and the fractional derivative order has meaningful effects on natural frequencies of the oscillator.
Keywords: Fractional differential equation, Caputo fractional derivative, vibration, van der Pol equation, multiple time scale, finite difference.