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      Differential Equations with Fractional Derivative and Universal Map with Memory

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          Abstract

          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 map from fractional differential equations, we use the equivalence of the Cauchy-type problems and to the nonlinear Volterra integral equations of 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 derivatives, are suggested.

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          Dielectric relaxation in solids

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            Nonlinear differential equations with the Caputo fractional derivative in the space of continuously differentiable functions

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              Fractional equations of Curie–von Schweidler and Gauss laws

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                Author and article information

                Journal
                21 July 2011
                Article
                10.1088/1751-8113/42/46/465102
                1107.4205
                49653e64-4de6-4034-871b-7876798e67c0

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                Journal of Physics A. Vol.42. No.46. (2009) 465102
                21 pages, LaTeX
                nlin.CD math-ph math.MP

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