Numerical behavior of the variable-order fractional Van der Pol oscillator

Abstract

In this article, we investigate the behavior of a Van der Pol oscillator based on the variable-order Caputo fractional derivatives. After variable-order fractional modeling, we discretize the obtained equations using the Legendre–Gauss–Lobatto points and employ Lagrange interpolating functions. An algebraic system is gained that approximates the variables and their fractional derivatives. Also, an approach is suggested to calculate the differentiation matrix related to the variable-order Caputo fractional derivative. Moreover, an algorithm is presented for solving the variable-order Caputo fractional Van der Pol equation on large time-interval. Numerical simulations are provided to represent the applicability of the suggested method and to see the treatment of variable-order Caputo fractional Van der Pol oscillator.