Discrete map with memory from fractional differential equation of arbitrary positive orderстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:Derivatives of fractional order with respect to time describe long-term memory effects. Using nonlinear differential equation with Caputo fractional derivative of arbitrary order alpha>0, we obtain discrete maps with power-law memory. These maps are generalizations of well-known universal map. The memory in these maps means that their present state is determined by all past states with power-law forms of weights. Discrete map equations are obtained by using the equivalence of the Cauchy-type problem for fractional differential equation and the nonlinear Volterra integral equation of the second kind.