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Approximation approach to periodic BVP for fractional differential systems

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Abstract

We give a new approach of investigation and approximation of solutions of fractional differential systems (FDS) subjected to periodic boundary conditions. According to the main idea of the numerical–analytic technique, we construct a sequence of functions that it proved to be convergent. It is shown that the limit function of the constructed sequence satisfies a modified FDS and periodic conditions. It is a solution of the given periodic BVP, if the corresponding determined equation has a root. An example of fractional Duffing equation is also presented to illustrate the theory.

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Authors and Affiliations

  1. Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava, Mlynská dolina, 842 48, Bratislava, Slovakia

    Michal Fečkan

  2. Mathematical Institute of Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Michal Fečkan

  3. Department of Differential Equations and Mathematical Physics, Uzhhorod National University, Narodna Square, 3, Uzhhorod, 88000, Ukraine

    Kateryna Marynets

Authors
  1. Michal Fečkan
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  2. Kateryna Marynets
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Correspondence to Michal Fečkan.

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Fečkan, M., Marynets, K. Approximation approach to periodic BVP for fractional differential systems. Eur. Phys. J. Spec. Top. 226, 3681–3692 (2017). https://doi.org/10.1140/epjst/e2018-00017-9

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  • DOI: https://doi.org/10.1140/epjst/e2018-00017-9

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