Interesting and complex behaviour of Duffing equations within the frame of Caputo fractional operator

Abstract

The coupled system exemplifying the damped and driven oscillators (namely, Duffing equations) is examined with a familiar and robust numerical method. In the framework, we hired a reliable and most cited Caputo fractional operator to capture essential and stimulating behaviours of the hired physical model. The existence of the solution for the considered model is presented, and we captured the nature of the strange attractor for the Duffing equations with a period of the driving force. The effect of chaotic nature associated parameter is illustrated. The essence of generalizing the classical models is presented with plots, and associated consequences are demonstrated for the substantial time period.