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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
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