Fractional Equations of Kicked Systems and Discrete Maps

Details Fractional Equations of Kicked Systems and Discrete Maps Fractional Equations of Kicked Systems and Discrete Maps

2011-07-20

arxiv.org/abs/1107.3953v1

Journal of Physics A 41 (2008) 435101

Nonlinear Sciences

Chaotic Dynamics

23 pages, LaTeX

Scientific paper

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.

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