Lag-synchronization of two different fractional-order time-delayed chaotic systems using fractional adaptive sliding mode controller

This paper investigates the lag-synchronization of two non-idantical fractional-order time-delayed chaotic systems in the presence of uncertainties and external disturbances. A fractional-order adaptive sliding mode control for lag-synchronizing two non-identical fractional-order time-delayed chaotic systems with unknown uncertainties, external disturbances and uncertain parameters is proposed. The suggested technique can be used for a large range of chaotic systems. Appropriate adaptive laws are established to overcome the uncertain parameters and bounds of parameters. Furthermore, to eliminate the undesirable phenomenon of chattering, instead of using the discontinuous sign function, the continuous tanh function with adaptive amplitude and slope is used. Using the Lyapunov theorem, the stability of the suggested strategy control is proved. Finally, the simulation results demonstrate the feasibility and robustness of our suggested scheme.