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Stability analysis of the set of trajectories for differential equations with fractional dynamics

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Abstract

In this paper we consider the problem of stability analysis of the set of trajectories for fractional differential equations under interval initial conditions. Sufficient conditions for Lyapunov-type stability and Mittag-Leffler stability are obtained based on some matrix auxiliary Lyapunov functions and a pseudo-linear representation of integral inequalities.

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Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics NAS of Ukraine, Nesterov str., 3, 03057, Kiev-57, Ukraine

    A. A. Martynyuk & Yu. A. Martynyuk-Chernienko

  2. University of Texas at San Antonio, Department of Mathematics, San Antonio, TX, 78249, USA

    I. Stamova

Authors
  1. A. A. Martynyuk
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  2. I. Stamova
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  3. Yu. A. Martynyuk-Chernienko
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Correspondence to I. Stamova.

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Martynyuk, A.A., Stamova, I. & Martynyuk-Chernienko, Y.A. Stability analysis of the set of trajectories for differential equations with fractional dynamics. Eur. Phys. J. Spec. Top. 226, 3609–3637 (2017). https://doi.org/10.1140/epjst/e2018-00051-7

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  • DOI: https://doi.org/10.1140/epjst/e2018-00051-7

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