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Functional Differential Equations with Piecewise Constant Argument

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Regularity and Stochasticity of Nonlinear Dynamical Systems

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 21))

Abstract

We introduce a new class of functional differential equations with functional response on piecewise constant argument, \({ FDEPCA}\). It contains functional differential equations with continuous time [21, 25, 28, 31] as well as differential equations with piecewise constant argument [1, 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17, 22, 22, 23]. We concentrate only on retarded equations, but one can easily extend the discussion to any type of piecewise constant argument and functional differential equations. Nonlinear and quasilinear systems are under consideration. At the end of the chapter, we suggest how one can apply the systems for solution of real-world problems, provided more general systems for future investigations.

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Authors and Affiliations

  1. Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey

    M. U. Akhmet

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  1. M. U. Akhmet
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  1. Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas, USA

    Dimitri Volchenkov

  2. Centre de Physique Théorique, Aix-Marseille Université, Marseille, France

    Xavier Leoncini

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Akhmet, M.U. (2018). Functional Differential Equations with Piecewise Constant Argument. In: Volchenkov, D., Leoncini, X. (eds) Regularity and Stochasticity of Nonlinear Dynamical Systems. Nonlinear Systems and Complexity, vol 21. Springer, Cham. https://doi.org/10.1007/978-3-319-58062-3_4

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  • DOI: https://doi.org/10.1007/978-3-319-58062-3_4

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