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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Main Author: B. Kh. Turmetov
Format: Article
Language:English
Published: Petrozavodsk State University 2024-11-01
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.
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institution Kabale University
issn 2306-3424
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publishDate 2024-11-01
publisher Petrozavodsk State University
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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