IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i9p1408-d1642484.html
   My bibliography  Save this article

Fundamental Matrix, Measure Resolvent Kernel and Stability Properties of Fractional Linear Delayed System with Discontinuous Initial Conditions

Author

Listed:
  • Hristo Kiskinov

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

  • Mariyan Milev

    (Faculty of Economics and Business Administration, Sofia University, 1504 Sofia, Bulgaria)

  • Milena Petkova

    (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

In the present work, a Cauchy (initial) problem for a fractional linear system with distributed delays and Caputo-type derivatives of incommensurate order is considered. As the main result, a new straightforward approach to study the considered initial problem via an equivalent Volterra–Stieltjes integral system is introduced. This approach is based on the existence and uniqueness of a global fundamental matrix for the corresponding homogeneous system, which allows us to prove that the corresponding resolvent system possesses a unique measure resolvent kernel. As a consequence, an integral representation of the solutions of the studied system is obtained. Then, using the obtained results, relations between the stability of the zero solution of the homogeneous system and different kinds of boundedness of its other solutions are established.

Suggested Citation

  • Hristo Kiskinov & Mariyan Milev & Milena Petkova & Andrey Zahariev, 2025. "Fundamental Matrix, Measure Resolvent Kernel and Stability Properties of Fractional Linear Delayed System with Discontinuous Initial Conditions," Mathematics, MDPI, vol. 13(9), pages 1-18, April.
  • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1408-:d:1642484
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/9/1408/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/13/9/1408/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1408-:d:1642484. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.