On a boundary value problem for the biharmonic equation with multiple involutions
Turmetov B. Karachik V. Muratbekova M.
September 2021MDPI AG
Mathematics
2021#9Issue 17
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.
Biharmonic equation , Boundary value problems , Fractional deriva-tive , Hadamard operator , Multiple involutions
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Department of Mathematics, Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkistan, 161200, Kazakhstan
Department of Mathematical Analysis, South Ural State University (NRU), Chelyabinsk, 454080, Russian Federation
Department of Mathematics
Department of Mathematical Analysis
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