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Starting from kicked equations of motion with derivatives of non-integerorders, we obtain "fractional" discrete maps. These maps are generalizations ofwell-known universal, standard, dissipative, kicked damped rotator maps. Themain property of the suggested fractional maps is a long-term memory. Thememory effects in the fractional discrete maps mean that their present stateevolution depends on all past states with special forms of weights. These formsare represented by combinations of power-law functions.

Fractional Equations of Kicked Systems and Discrete Maps