Abstract
In this work, we exemplify the behaviour of the nonlinear model of arbitrary order differential equations by adopting q-homotopy analysis transform method (q-HATM). In the present study, the illustrated scheme is a graceful amalgamation of Laplace transform with q-homotopy analysis algorithm and we considered arbitrary order derivative using Atangana-Baleanu (AB) operator. The suggested nonlinear system exhibits chaotic behaviour in nature with respect to considered initial conditions. Fixed point hypothesis heard present the existence and uniqueness for the attained solution. We exemplified suggested arbitrary order system with to illustrate and confirm the efficiency of the projected solution procedure. Further, the numerical simulation is illustrated and also the chaotic behaviour of the obtained result captured with respect to arbitrary order in terms of plots. The obtained results confirm the projected scheme is highly methodical, easy to implement and very powerful to exemplify the nature of the dynamical system of arbitrary order.