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Stability of fractional-order systems with Prabhakar derivatives

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Abstract

Fractional derivatives of Prabhakar type are capturing an increasing interest since their ability to describe anomalous relaxation phenomena (in dielectrics and other fields) showing a simultaneous nonlocal and nonlinear behaviour. In this paper we study the asymptotic stability of systems of differential equations with the Prabhakar derivative, providing an exact characterization of the corresponding stability region. Asymptotic expansions (for small and large arguments) of the solution of linear differential equations of Prabhakar type and a numerical method for nonlinear systems are derived. Numerical experiments are hence presented to validate theoretical findings.

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Authors and Affiliations

  1. Department of Mathematics, University of Bari, Via E. Orabona 4, 70126, Bari, Italy

    Roberto Garrappa

  2. INdAM Research Group GNCS, Rome, Italy

    Roberto Garrappa

  3. Department of Mathematics and Computer Science, West University of Timişoara, Bd. V. Pârvan 4, 300223, Timişoara, Romania

    Eva Kaslik

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  1. Roberto Garrappa
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Correspondence to Eva Kaslik.

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This research was funded by the COST Action CA 15225 - “Fractional-order systems- analysis, synthesis and their importance for future design”. The work of R. Garrappa was also partially supported by a GNCS-INdAM 2020 Project.

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Garrappa, R., Kaslik, E. Stability of fractional-order systems with Prabhakar derivatives. Nonlinear Dyn 102, 567–578 (2020). https://doi.org/10.1007/s11071-020-05897-9

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