Differential equations with fractional derivative and universal map with memoryстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:Discrete maps with long-term memory are obtained from nonlinear differential equations with Riemann-Liouville and Caputo fractional derivatives. These maps are generalizations of the well-known universal map. The memory means that their present state is determined by all past states with special forms of weights. To obtain discrete maps from fractional differential equations, we use the equivalence of the Cauchy-type problems and to the nonlinear Volterra integral equations of the second kind. General forms of the universal maps with memory, which take into account general initial conditions for the cases of the Riemann-Liouville and Caputo fractional derivative, are suggested.