ON SOLVABILITY OF SOME BOUNDARY-VALUE PROBLEMS FOR THE NON-LOCAL POISS
In this paper, a non-local analogue of the Laplace operator is introduced using involution-type mappings. For the corresponding non-local analogue of the Poisson equation in the unit ball, two types of boundary-value problems are considered. In the studied problems, the boundary conditions involve f...
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Petrozavodsk State University
2024-11-01
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| Series: | Проблемы анализа |
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| Online Access: | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=16550&lang=en |
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| author | B. Kh. Turmetov |
| author_facet | B. Kh. Turmetov |
| author_sort | B. Kh. Turmetov |
| collection | DOAJ |
| description | In this paper, a non-local analogue of the Laplace operator is introduced using involution-type mappings. For the corresponding non-local analogue of the Poisson equation in the unit ball, two types of boundary-value problems are considered. In the studied problems, the boundary conditions involve fractional-order operators with derivatives of the Hadamard type. The first problem
generalizes the well-known Dirichlet, Neumann, and Robin problems for fractional-order boundary operators. The second problem is a generalization of periodic and antiperiodic boundary-value problems for circular domains. Theorems on the existence and uniqueness of solutions to the studied problems are proved. Exact conditions for solvability of the studied problems are found, and integral representations of the solutions are obtained. |
| format | Article |
| id | doaj-art-94e879ef1434448f941b964c34fee03a |
| institution | Kabale University |
| issn | 2306-3424 2306-3432 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Petrozavodsk State University |
| record_format | Article |
| series | Проблемы анализа |
| spelling | doaj-art-94e879ef1434448f941b964c34fee03a2025-01-28T11:08:14ZengPetrozavodsk State UniversityПроблемы анализа2306-34242306-34322024-11-0113 (31)311813410.15393/j3.art.2024.16550ON SOLVABILITY OF SOME BOUNDARY-VALUE PROBLEMS FOR THE NON-LOCAL POISSB. Kh. Turmetov0Khoja Akhmet Yassawi International Kazakh-Turkish University, Alfraganus University 2a Yukori Karakamish Str.In this paper, a non-local analogue of the Laplace operator is introduced using involution-type mappings. For the corresponding non-local analogue of the Poisson equation in the unit ball, two types of boundary-value problems are considered. In the studied problems, the boundary conditions involve fractional-order operators with derivatives of the Hadamard type. The first problem generalizes the well-known Dirichlet, Neumann, and Robin problems for fractional-order boundary operators. The second problem is a generalization of periodic and antiperiodic boundary-value problems for circular domains. Theorems on the existence and uniqueness of solutions to the studied problems are proved. Exact conditions for solvability of the studied problems are found, and integral representations of the solutions are obtained.https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=16550&lang=ennon-local equationfractional derivativehadamard operatorperiodic problemdirichlet problemneumann problem |
| spellingShingle | B. Kh. Turmetov ON SOLVABILITY OF SOME BOUNDARY-VALUE PROBLEMS FOR THE NON-LOCAL POISS Проблемы анализа non-local equation fractional derivative hadamard operator periodic problem dirichlet problem neumann problem |
| title | ON SOLVABILITY OF SOME BOUNDARY-VALUE PROBLEMS FOR THE NON-LOCAL POISS |
| title_full | ON SOLVABILITY OF SOME BOUNDARY-VALUE PROBLEMS FOR THE NON-LOCAL POISS |
| title_fullStr | ON SOLVABILITY OF SOME BOUNDARY-VALUE PROBLEMS FOR THE NON-LOCAL POISS |
| title_full_unstemmed | ON SOLVABILITY OF SOME BOUNDARY-VALUE PROBLEMS FOR THE NON-LOCAL POISS |
| title_short | ON SOLVABILITY OF SOME BOUNDARY-VALUE PROBLEMS FOR THE NON-LOCAL POISS |
| title_sort | on solvability of some boundary value problems for the non local poiss |
| topic | non-local equation fractional derivative hadamard operator periodic problem dirichlet problem neumann problem |
| url | https://issuesofanalysis.petrsu.ru/article/genpdf.php?id=16550&lang=en |
| work_keys_str_mv | AT bkhturmetov onsolvabilityofsomeboundaryvalueproblemsforthenonlocalpoiss |