This study introduces two 4D and 5D laser chaotic systems, including the regularized Prabhakar fractional derivative with incommensurate parameters, and investigates their properties and complex dynamics. The system’s chaotic vibration is then controlled via a feedback control approach. Furthermore, we demonstrate that the parameters of the regularized Prabhakar fractional derivative have a significant impact on the stability and chaotic behavior of the systems. The numerical simulation results show that systems with the regularized Prabhakar fractional derivative are more stable than the integer order systems or the fractional systems with the Caputo fractional derivative. Furthermore, two identical regularized Prabhakar fractional laser chaotic systems are synchronized by the design of control laws.
