On a Boundary Value Problem for the Biharmonic Equation with Multiple Involutions
| Autor: | Valery Karachik, Moldir A. Muratbekova, Batirkhan Kh. Turmetov |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
biharmonic equation boundary value problems General Mathematics multiple involutions Boundary (topology) fractional derivative Type (model theory) Hadamard operator Dirichlet distribution Fractional calculus symbols.namesake Operator (computer programming) Computer Science (miscellaneous) Biharmonic equation symbols QA1-939 Boundary value problem Uniqueness Engineering (miscellaneous) Mathematics |
| Zdroj: | Mathematics Volume 9 Issue 17 Mathematics, Vol 9, Iss 2020, p 2020 (2021) |
| ISSN: | 2227-7390 |
| DOI: | 10.3390/math9172020 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|