IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i17p2020-d620467.html
   My bibliography  Save this article

On a Boundary Value Problem for the Biharmonic Equation with Multiple Involutions

Author

Listed:
  • Batirkhan Turmetov

    (Department of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan 161200, Kazakhstan
    These authors contributed equally to this work.)

  • Valery Karachik

    (Department of Mathematical Analysis, South Ural State University (NRU), 454080 Chelyabinsk, Russia
    These authors contributed equally to this work.)

  • Moldir Muratbekova

    (Department of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan 161200, Kazakhstan
    These authors contributed equally to this work.)

Abstract

A nonlocal analogue of the biharmonic operator with involution-type transformations was considered. For the corresponding biharmonic equation with involution, we investigated the solvability of boundary value problems with a fractional-order boundary operator having a derivative of the Hadamard-type. First, transformations of the involution type were considered. The properties of the matrices of these transformations were investigated. As applications of the considered transformations, the questions about the solvability of a boundary value problem for a nonlocal biharmonic equation were studied. Modified Hadamard derivatives were considered as the boundary operator. The considered problems covered the Dirichlet and Neumann-type boundary conditions. Theorems on the existence and uniqueness of solutions to the studied problems were proven.

Suggested Citation

  • Batirkhan Turmetov & Valery Karachik & Moldir Muratbekova, 2021. "On a Boundary Value Problem for the Biharmonic Equation with Multiple Involutions," Mathematics, MDPI, vol. 9(17), pages 1-23, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:17:p:2020-:d:620467
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/17/2020/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/17/2020/
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:9:y:2021:i:17:p:2020-:d:620467. 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.