Fractional Equations of Kicked Systems and Discrete Maps

Abstract

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.

23 pages, LaTeX

References in corpus (3)

• Fractional Variations for Dynamical Systems: Hamilton and Lagrange Approaches
• Long-term memory contribution as applied to the motion of discrete dynamical systems
• Chains with Fractal Dispersion Law

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