Chaos synchronization of fractional chaotic maps based on the stability condition

•Discrete fractional chaotic maps are proposed in the Riemann–Liouville’s sense.•Chaos synchronization of the map is designed and the control parameters are selected according to the stability conditions.•The feedback control method is extended to discrete fractional equations.

In the fractional calculus, one of the main challenges is to find suitable models which are properly described by discrete derivatives with memory. Fractional Logistic map and fractional Lorenz maps of Riemann–Liouville type are proposed in this paper. The general chaotic behaviors are investigated in comparison with the Caputo one. Chaos synchronization is designed according to the stability results. The numerical results show the method’s effectiveness and fractional chaotic map’s potential role for secure communication.