  This paper is devoted to the memory of Professor George M. Zaslavsky passed
away on November 25, 2008. In the field of discrete maps, George M. Zaslavsky
introduced a dissipative standard map which is called now the Zaslavsky map. G.
Zaslavsky initialized many fundamental concepts and ideas in the fractional
dynamics and kinetics. In this paper, starting from kicked damped equations
with derivatives of non-integer orders we derive a fractional generalization of
discrete maps. These fractional maps are generalizations of the Zaslavsky map
and the Henon map. The main property of the fractional differential equations
and the correspondent fractional maps is a long-term memory and dissipation.
The memory is realized by the fact that their present state evolution depends
on all past states with special forms of weights.
