On fractional–order discrete–time systems: Chaos, stabilization and synchronization

•Three fractional-order discrete chaotic maps are proposed.•Important dynamics of three maps are investigated.•A stabilizing strategy is introduced for the proposed maps.•A combined synchronization scheme is presented. In this paper, we propose three systems, namely the fractional Lozi map, the fractional Lorenz map, and the fractional flow map. We study some of the important dynamics of these maps including the bifurcation graphs. In addition, we propose control laws aimed at stabilizing and synchronizing a combination of these three maps. The convergence of the stabilized states and the synchronization errors is established by means of the linearization method. Numerical simulations are also presented to confirm the main findings of the study.