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

Batirkhan Turmetov, Valery Karachik and Moldir Muratbekova
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Batirkhan Turmetov: Department of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan 161200, Kazakhstan
Valery Karachik: Department of Mathematical Analysis, South Ural State University (NRU), 454080 Chelyabinsk, Russia
Moldir Muratbekova: Department of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan 161200, Kazakhstan

Mathematics, 2021, vol. 9, issue 17, 1-23

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.

Keywords: boundary value problems; biharmonic equation; multiple involutions; fractional derivative; Hadamard operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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