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ANALYSIS OF APPROXIMATE SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS IN THEIR GENERAL FORM WITH GENERALIZED ORDER

In this paper, we dedicate our study on the approximate solutions of van der Pol equation in their general form. First, we prove the approximate analytic solutions to this equation by different perturbation methods, simple perturbation method (SPM), Lindstedt-Poincaré method (PLM) and Averaging method (AM). Then we compare these approximations with each other and with the exact solution. Second, we introduce a new form of generalized Van Der Pol oscillator with fractional-order derivatives. Which is analyzed through phase portraits, Poincaré maps and analytic solutions, we use numerical simulation to illustrate the behavior of the fractional order system.