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Asymptotic behavior of solutions of linear multi-order fractional differential systems

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Abstract

In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential equation systems. Next, a representation of solutions of homogeneous linear multi-order fractional differential equation systems in series form is provided. Finally, we give characteristics regarding the asymptotic behavior of solutions to some classes of linear multi-order fractional differential equation systems.

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Authors and Affiliations

  1. GNS mbH Gesellschaft für numerische Simulation mbH, Am Gaußberg, 2, 38114, Braunschweig-, Germany

    Kai Diethelm

  2. AG Numerik, Institut Computational Mathematics, Technische Universität Braunschweig, Universitätsplatz 2, 38106, Braunschweig-, Germany

    Kai Diethelm

  3. Center for Dynamics & Institute for Analysis, Department of Mathematics, Technische Universität Dresden, 01062, Dresden-, Germany

    Stefan Siegmund

  4. Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, 10307, Ha Noi-, Vietnam

    H. T. Tuan

Authors
  1. Kai Diethelm
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  2. Stefan Siegmund
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  3. H. T. Tuan
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Correspondence to Kai Diethelm.

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Dedicated to Professor Virginia Kiryakova on the occasion of her 65th birthday and the 20th anniversary of FCAA

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Diethelm, K., Siegmund, S. & Tuan, H.T. Asymptotic behavior of solutions of linear multi-order fractional differential systems. FCAA 20, 1165–1195 (2017). https://doi.org/10.1515/fca-2017-0062

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  • DOI: https://doi.org/10.1515/fca-2017-0062

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