In this chapter, we introduce a new chaotic autonomous system with the fractional regularized Prabhakar derivative. Then, we prove the existence and uniqueness of the solution to the mentioned system. We also give a numerical scheme for the system and state a theorem to analyze the stability of the system based on the Lyapunov second method. Next, we eliminate the chaotic behaviors of the system by means of a feedback controller and presented theorem. Moreover, synchronization is achieved between two regularized Prabhakar fractional chaotic autonomous systems. We further present numerical simulations and reveal asymptotic stability and chaotic behaviors of the system to verify the theoretical analysis. Furthermore, we show that the parameters of the fractional regularized Prabhakar derivative play the important role in the dynamic behaviors of the system and the chaotic behavior reduces and even eliminates by choosing the appropriate parameters of the fractional regularized Prabhakar derivative in the system
