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Integral Representation for the Solutions of Autonomous Linear Neutral Fractional Systems with Distributed Delay

Author

Listed:
  • Ekaterina Madamlieva

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

  • Mihail Konstantinov

    (Department of Mathematics, University of Architecture, Civil Engineering and Geodesy, 1046 Sofia, Bulgaria)

  • Marian Milev

    (Department of Matematics and Physics, University Of Food Technology, 4000 Plovdiv, Bulgaria)

  • Milena Petkova

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

Abstract

The aim of this work is to obtain an integral representation formula for the solutions of initial value problems for autonomous linear fractional neutral systems with Caputo type derivatives and distributed delays. The results obtained improve and extend the corresponding results in the particular case of fractional systems with constant delays and will be a useful tool for studying different kinds of stability properties. The proposed results coincide with the corresponding ones for first order neutral linear differential systems with integer order derivatives.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:364-:d:329595
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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. Li, Mengmeng & Wang, JinRong, 2018. "Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 254-265.
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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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