Dynamical behaviors, circuit realization, chaos control, and synchronization of a new fractional order hyperchaotic system

In this study, we introduce a new fractional order hyperchaotic system. We prove the existence and uniqueness of the solution to the proposed system. We also study the stability of the system's equilibrium points and the continuous dependence of the system's solution on the initial conditions. The dynamical behavior of the system is explored and a circuit implementation of the fractional order system is proposed. We examine the effects of fractional order derivatives on chaos control for the proposed system. examined. Finally, synchronization is achieved between two fractional order hyperchaotic systems using a linear feedback controller and a time-delayed feedback controller. Numerical simulations are presented that verify the theoretical analysis.