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Non-Instantaneous Impulses in Caputo Fractional Differential Equations

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Abstract

Recent modeling of real world phenomena give rise to Caputo type fractional order differential equations with non-instantaneous impulses. The main goal of the survey is to highlight some basic points in introducing non-instantaneous impulses in Caputo fractional differential equations. In the literature there are two approaches in interpretation of the solutions. Both approaches are compared and their advantages and disadvantages are illustrated with examples. Also some existence results are derived.

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Authors and Affiliations

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

    Ravi Agarwal

  2. Department of Applied Mathematics, University of Plovdiv Paisii Hilendarski, Plovdiv, Bulgaria

    Snezhana Hristova

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

    Donal O’Regan

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  1. Ravi Agarwal
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  2. Snezhana Hristova
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  3. Donal O’Regan
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Correspondence to Ravi Agarwal.

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Agarwal, R., Hristova, S. & O’Regan, D. Non-Instantaneous Impulses in Caputo Fractional Differential Equations. FCAA 20, 595–622 (2017). https://doi.org/10.1515/fca-2017-0032

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