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

• Main Authors: Batirkhan Turmetov, Valery Karachik, Moldir Muratbekova
• Format: Article
• Language: English
• Published: MDPI AG 2021-08-01
• Series: Mathematics
• Subjects: boundary value problems; biharmonic equation; multiple involutions; fractional derivative; Hadamard operator
• Online Access: https://www.mdpi.com/2227-7390/9/17/2020

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.