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This work introduces the tool of discrete fractional calculus (DFC) in recent applications. It is used to introduce memory effects into discrete maps. General Chaotic behaviors are shown. Image encryption of fractional order is illustrated as one of the possible applications. Furthermore, chaos synchronization is designed according to stability conditions. Finally, a Riesz-Caputo fractional difference is given by use of both left and right Caputo-like fractional differences. Modelling of the diffusion on discrete domains is shown.