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Mittag–Leffler Stability for Impulsive Caputo Fractional Differential Equations

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Abstract

The stability properties of Caputo fractional differential equations with impulses are studied. Both types of impulses, non-instantaneous impulses as well as instantaneous impulses are considered. The two approaches in the literature for the interpretation ofsolutions of impulsive Caputo fractional differential equations are presented and discussed. A generalization of Mittag–Leffler stability with respect to both types of impulses is given.

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Authors and Affiliations

  1. Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX, 78363, USA

    R. Agarwal

  2. Plovdiv University, Tzar Asen 24, 4000, Plovdiv, Bulgaria

    S. Hristova

  3. School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

    D. O’Regan

Authors
  1. R. Agarwal
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  2. S. Hristova
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  3. D. O’Regan
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Correspondence to R. Agarwal.

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Agarwal, R., Hristova, S. & O’Regan, D. Mittag–Leffler Stability for Impulsive Caputo Fractional Differential Equations. Differ Equ Dyn Syst 29, 689–705 (2021). https://doi.org/10.1007/s12591-017-0384-4

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  • DOI: https://doi.org/10.1007/s12591-017-0384-4

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