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Mathematics
Volume 9
Issue 17
10.3390/math9172020
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Article

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

by
Batirkhan Turmetov
1,*,†,
Valery Karachik
2,† and
Moldir Muratbekova
1,†
1
Department of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan 161200, Kazakhstan
2
Department of Mathematical Analysis, South Ural State University (NRU), 454080 Chelyabinsk, Russia
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2021, 9(17), 2020; https://doi.org/10.3390/math9172020
Submission received: 29 July 2021 / Revised: 16 August 2021 / Accepted: 18 August 2021 / Published: 24 August 2021
(This article belongs to the Special Issue Functional Differential Equations and Applications 2020)
Versions Notes

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 boundary value problems; biharmonic equation; multiple involutions; fractional derivative; Hadamard operator

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MDPI and ACS Style

Turmetov, B.; Karachik, V.; Muratbekova, M. On a Boundary Value Problem for the Biharmonic Equation with Multiple Involutions. Mathematics 2021, 9, 2020. https://doi.org/10.3390/math9172020

AMA Style

Turmetov B, Karachik V, Muratbekova M. On a Boundary Value Problem for the Biharmonic Equation with Multiple Involutions. Mathematics. 2021; 9(17):2020. https://doi.org/10.3390/math9172020

Chicago/Turabian Style

Turmetov, Batirkhan, Valery Karachik, and Moldir Muratbekova. 2021. "On a Boundary Value Problem for the Biharmonic Equation with Multiple Involutions" Mathematics 9, no. 17: 2020. https://doi.org/10.3390/math9172020

APA Style

Turmetov, B., Karachik, V., & Muratbekova, M. (2021). On a Boundary Value Problem for the Biharmonic Equation with Multiple Involutions. Mathematics, 9(17), 2020. https://doi.org/10.3390/math9172020

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