Fractional Stochastic Van der Pol Oscillator with Piecewise Derivatives

Abstract

This work investigates piecewise Vand der Pol oscillator under the arbitrary order, piecewise derivatives, and power nonlinearities to present a novel idea of piecewise systems using the classical-power-law randomness and classical Mittag–Leffler-law-randomness. We are able to study the dynamics of piecewise Van der Pol oscillators because the oscillator is one of the prototype models of the systems. It has become famous for examining the dynamics of the systems. To obtain the approximate solution for the aforementioned system, the famous Adams–Bashforth method is applied. The algorithm for obtaining numerical solutions is presented as well as the obtained results were presented graphically along with their different behavior. This oscillator is successfully applied to the model, a diversity of physical processes like nonlinear electronic circuits. Despite the simplicity of this oscillator, the behavior of the models is extremely prosperous and research is still ongoing.