A numerical study of the Van der Pol model derived by the Caputo–Fabrizio operator

Abstract

The study of nonlinear oscillators is an important topic in the development of the theory of dynamical systems. In this research, a nonlinear fractional model is introduced, which is called the fractional Van der Pol model. This modified model is derived using the Caputo–Fabrizio operator. Achieving the solution of this model is not easy. Therefore, in this research, an efficient algorithm for solving this fractional model is evaluated. This algorithm is supported by the three-step Adams–Bashforth process. A significant feature of this research is the graphical presentation of achieving limit cycles for various parameters.