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Existence of Absolutely Continuous Fundamental Matrix of Linear Fractional System with Distributed Delays

Author

Listed:
  • Hristo Kiskinov

    (Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria)

  • Ekaterina Madamlieva

    (Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria)

  • Magdalena Veselinova

    (Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria)

  • Andrey Zahariev

    (Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria)

Abstract

The goal of the present paper is to obtain sufficient conditions that guaranty the existence and uniqueness of an absolutely continuous fundamental matrix for a retarded linear fractional differential system with Caputo type derivatives and distributed delays. Some applications of the obtained result concerning the integral representation of the solutions are given too.

Suggested Citation

  • Hristo Kiskinov & Ekaterina Madamlieva & Magdalena Veselinova & Andrey Zahariev, 2021. "Existence of Absolutely Continuous Fundamental Matrix of Linear Fractional System with Distributed Delays," Mathematics, MDPI, vol. 9(2), pages 1-18, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:2:p:150-:d:478889
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    References listed on IDEAS

    as
    1. Hai Zhang & Jinde Cao & Wei Jiang, 2013. "General Solution of Linear Fractional Neutral Differential Difference Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-7, June.
    2. Andrey Zahariev & Hristo Kiskinov, 2020. "Asymptotic Stability of the Solutions of Neutral Linear Fractional System with Nonlinear Perturbation," Mathematics, MDPI, vol. 8(3), pages 1-18, March.
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    Citations

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    Cited by:

    1. Hristo Kiskinov & Mariyan Milev & Andrey Zahariev, 2022. "About the Resolvent Kernel of Neutral Linear Fractional System with Distributed Delays," Mathematics, MDPI, vol. 10(23), pages 1-17, December.
    2. Ekaterina Madamlieva & Marian Milev & Tsvetana Stoyanova, 2023. "On Stability Criteria Induced by the Resolvent Kernel for a Fractional Neutral Linear System with Distributed Delays," Mathematics, MDPI, vol. 11(3), pages 1-21, January.

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    1. Hristo Kiskinov & Mariyan Milev & Andrey Zahariev, 2022. "About the Resolvent Kernel of Neutral Linear Fractional System with Distributed Delays," Mathematics, MDPI, vol. 10(23), pages 1-17, December.
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    4. Ekaterina Madamlieva & Mihail Konstantinov & Marian Milev & Milena Petkova, 2020. "Integral Representation for the Solutions of Autonomous Linear Neutral Fractional Systems with Distributed Delay," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    5. Ekaterina Madamlieva & Marian Milev & Tsvetana Stoyanova, 2023. "On Stability Criteria Induced by the Resolvent Kernel for a Fractional Neutral Linear System with Distributed Delays," Mathematics, MDPI, vol. 11(3), pages 1-21, January.

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