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Existence and uniqueness of solution for a class of nonlinear sequential differential equations of fractional order

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Central European Journal of Mathematics

Abstract

Two-term semi-linear and two-term nonlinear fractional differential equations (FDEs) with sequential Caputo derivatives are considered. A unique continuous solution is derived using the equivalent norms/metrics method and the Banach theorem on a fixed point. Both, the unique general solution connected to the stationary function of the highest order derivative and the unique particular solution generated by the initial value problem, are explicitly constructed and proven to exist in an arbitrary interval, provided the nonlinear terms fulfil the corresponding Lipschitz condition. The existence-uniqueness results are given for an arbitrary order of the FDE and an arbitrary partition of orders between the components of sequential derivatives.

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Authors and Affiliations

  1. Institute of Mathematics, Częstochowa University of Technology, Dąbrowskiego 73, 42-200, Częstochowa, Poland

    Małgorzata Klimek & Marek Błasik

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  1. Małgorzata Klimek
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  2. Marek Błasik
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Correspondence to Małgorzata Klimek.

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Klimek, M., Błasik, M. Existence and uniqueness of solution for a class of nonlinear sequential differential equations of fractional order. centr.eur.j.math. 10, 1981–1994 (2012). https://doi.org/10.2478/s11533-012-0112-9

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  • DOI: https://doi.org/10.2478/s11533-012-0112-9

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