The hybrid control law incorporating adaptive backstepping is suggested for the synchronization of two identical modified piecewise Rossler models. The suggested approach gives rapid, high rigorous chaos synchronization in the presence of external disturbances and unknown system parameters. The adaptive backstepping control approach is established to stabilize the dynamics of synchronization error occurring from the conflict (mismatch) between the response and drive systems. The unknown external disturbance and unknown system parameters are determined by the adaptive backstepping law in such a way that the whole system, with the controller, stabilizes. Performance of the suggested law is examined for a numerical solution and compared against frequently utilized chaos synchronization approaches including active control, optimal control, and adaptive backstepping control approach. It was investigated
for the aspect of chaos synchronization and synchronization errors. The synchronization of models via hybrid adaptive backstepping for the comparison of different derivatives with a novel MABC fractional operator is exhibited. The MABC fractional operator is a nonsingular operator obtained by integration by parts of the standard fractional operator with the Mittag–Leffler kernel. An effective approach is suggested for stabilizing chaos. Computer simulation results demonstrate the superior performance of the hybrid control approach over the state of the art for the synchronization of modified Rossler models.