Fractional study of a novel hyper-chaotic model involving single non-linearity

The applications of hyperchaotic systems (HCSs) can be widely seen in diverse fields associated with engineering due to their complicated dynamics, randomness, and high delicacy and sensibility. In the present work, we aim to investigate a new hyper-chaotic system involving a single non-linearity under the fractional Caputo–Fabrizio (CF) derivative for the first time. In fact, there is no previous study using fractional derivatives in this system. A new mathematical system using a fractional-order operator will be designed with the novel operator. The Caputo–Fabrizio non-integer operator is aimed to be employed to capture complex nature. In order to solve the extracted dynamical system, a quadratic numerical scheme is applied. This study contains stability and convergence sections for the considered method. Moreover, numerical results of the problem under various values of fractional orders and different values of initial conditions (ICs) are provided to show the performance of the suggested scheme. Figures of solutions for each dependent variable can be observed.