A dynamical study of the fractional order King Cobra model

In this chapter, we investigate the King Cobra face-shaped model under Caputo's fractional derivative and fractional conformable derivative in the Liouville–Caputo (LC) sense. The purpose of this research is to explore how the arbitrary order parameters influence the proposed chaotic model's behavior. Initially, we consider the model with the Caputo derivative and provide a special iterative solution using the Laplace transform. Furthermore, we propose the King Cobra model with a fractional conformable derivative in the LC case. To achieve the numerical result, a new Atangana–Seda numerical strategy based on Newton polynomials is shown for the Caputo derivative, while an Adams–Moulton type numerical approach is presented for the fractional conformable derivative. Lastly, several graphical simulations with varying fractional parameters are offered.