IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i13p1942-d1420283.html
   My bibliography  Save this article

Global Existence of Small Data Solutions to Weakly Coupled Systems of Semi-Linear Fractional σ –Evolution Equations with Mass and Different Nonlinear Memory terms

Author

Listed:
  • Seyyid Ali Saiah

    (Laboratory of Mathematics and Applications, Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University, Ouled Fares, Chlef 021800, Algeria)

  • Abdelatif Kainane Mezadek

    (Laboratory of Mathematics and Applications, Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University, Ouled Fares, Chlef 021800, Algeria)

  • Mohamed Kainane Mezadek

    (Laboratory of Mathematics and Applications, Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University, Ouled Fares, Chlef 021800, Algeria)

  • Abdelhamid Mohammed Djaouti

    (Preparatory Year, King Faisal University, Hofuf 31982, Saudi Arabia
    Department of Mathematics and Statistics, Faculty of Sciences, King Faisal University, Hofuf 31982, Saudi Arabia)

  • Ashraf Al-Quran

    (Preparatory Year, King Faisal University, Hofuf 31982, Saudi Arabia
    Department of Mathematics and Statistics, Faculty of Sciences, King Faisal University, Hofuf 31982, Saudi Arabia)

  • Ali M. A. Bany Awad

    (Deanship of Development and Quality Assurance, King Faisal University, Al-Ahsa 31982, Saudi Arabia)

Abstract

We study in this paper the long-term existence of solutions to the system of weakly coupled equations with fractional evolution and various nonlinearities. Our objective is to determine the connection between the regularity assumptions on the initial data, the memory terms, and the permissible range of exponents in a specific equation. Using L p − L q estimates for solutions to the corresponding linear fractional σ –evolution equations with vanishing right-hand sides, and applying a fixed-point argument, the existence of small data solutions is established for some admissible range of powers ( p 1 , p 2 , … , p k ) .

Suggested Citation

  • Seyyid Ali Saiah & Abdelatif Kainane Mezadek & Mohamed Kainane Mezadek & Abdelhamid Mohammed Djaouti & Ashraf Al-Quran & Ali M. A. Bany Awad, 2024. "Global Existence of Small Data Solutions to Weakly Coupled Systems of Semi-Linear Fractional σ –Evolution Equations with Mass and Different Nonlinear Memory terms," Mathematics, MDPI, vol. 12(13), pages 1-20, June.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:1942-:d:1420283
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/13/1942/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/12/13/1942/
    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:12:y:2024:i:13:p:1942-:d:1420283. 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.