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