On solvability of some boundary value problems for the non-local polyharmonic equation with boundary operators of the hadamard type
In this paper the solvability problems of some boundary value problems for a non-local polyharmonic equation are studied. A non-local polyharmonic equation is represented by using some orthogonal matrix. The properties and examples of such matrices are given. In the current boundary value problem, w...
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| Format: | Conference or Workshop Item |
| Language: | English |
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IOP Publishing
2019
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| Online Access: | http://umpir.ump.edu.my/id/eprint/27902/ http://umpir.ump.edu.my/id/eprint/27902/1/On%20solvability%20of%20some%20boundary%20value%20problems.pdf |
| _version_ | 1848822915765633024 |
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| author | Turmetov, Batirkhan Muratbekova, Moldir Ahmedov, Anvarjon A. |
| author_facet | Turmetov, Batirkhan Muratbekova, Moldir Ahmedov, Anvarjon A. |
| author_sort | Turmetov, Batirkhan |
| building | UMP Institutional Repository |
| collection | Online Access |
| description | In this paper the solvability problems of some boundary value problems for a non-local polyharmonic equation are studied. A non-local polyharmonic equation is represented by using some orthogonal matrix. The properties and examples of such matrices are given. In the current boundary value problem, which being considered in the paper, the fractional order differentiation operators are used as boundary operators. These operators are defined as derivatives of the Hadamard-Caputo type. Note that in particular cases of the parameters of the boundary conditions we obtain well known conditions of the Dirichlet, Neumann, and Robin type problems. For the problems under consideration, theorems on the existence and uniqueness of solutions are proved. The exact solvability conditions for the problem under study are found. In addition, we obtained representation for the solution of the fractional boundary problem for polyharmonic operator. |
| first_indexed | 2025-11-15T02:48:50Z |
| format | Conference or Workshop Item |
| id | ump-27902 |
| institution | Universiti Malaysia Pahang |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T02:48:50Z |
| publishDate | 2019 |
| publisher | IOP Publishing |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | ump-279022021-01-18T07:09:20Z http://umpir.ump.edu.my/id/eprint/27902/ On solvability of some boundary value problems for the non-local polyharmonic equation with boundary operators of the hadamard type Turmetov, Batirkhan Muratbekova, Moldir Ahmedov, Anvarjon A. QA Mathematics In this paper the solvability problems of some boundary value problems for a non-local polyharmonic equation are studied. A non-local polyharmonic equation is represented by using some orthogonal matrix. The properties and examples of such matrices are given. In the current boundary value problem, which being considered in the paper, the fractional order differentiation operators are used as boundary operators. These operators are defined as derivatives of the Hadamard-Caputo type. Note that in particular cases of the parameters of the boundary conditions we obtain well known conditions of the Dirichlet, Neumann, and Robin type problems. For the problems under consideration, theorems on the existence and uniqueness of solutions are proved. The exact solvability conditions for the problem under study are found. In addition, we obtained representation for the solution of the fractional boundary problem for polyharmonic operator. IOP Publishing 2019 Conference or Workshop Item PeerReviewed pdf en cc_by http://umpir.ump.edu.my/id/eprint/27902/1/On%20solvability%20of%20some%20boundary%20value%20problems.pdf Turmetov, Batirkhan and Muratbekova, Moldir and Ahmedov, Anvarjon A. (2019) On solvability of some boundary value problems for the non-local polyharmonic equation with boundary operators of the hadamard type. In: Journal of Physics: Conference Series, 2nd International Conference on Applied & Industrial Mathematics and Statistics (ICoAIMS 2019) , 23-25 July 2019 , Kuantan, Pahang, Malaysia. pp. 1-8., 1366 (012065). ISSN 1742-6588 (print); 1742-6596 (online) (Published) https://doi.org/10.1088/1742-6596/1366/1/012065 |
| spellingShingle | QA Mathematics Turmetov, Batirkhan Muratbekova, Moldir Ahmedov, Anvarjon A. On solvability of some boundary value problems for the non-local polyharmonic equation with boundary operators of the hadamard type |
| title | On solvability of some boundary value problems for the non-local polyharmonic equation with boundary operators of the hadamard type |
| title_full | On solvability of some boundary value problems for the non-local polyharmonic equation with boundary operators of the hadamard type |
| title_fullStr | On solvability of some boundary value problems for the non-local polyharmonic equation with boundary operators of the hadamard type |
| title_full_unstemmed | On solvability of some boundary value problems for the non-local polyharmonic equation with boundary operators of the hadamard type |
| title_short | On solvability of some boundary value problems for the non-local polyharmonic equation with boundary operators of the hadamard type |
| title_sort | on solvability of some boundary value problems for the non-local polyharmonic equation with boundary operators of the hadamard type |
| topic | QA Mathematics |
| url | http://umpir.ump.edu.my/id/eprint/27902/ http://umpir.ump.edu.my/id/eprint/27902/ http://umpir.ump.edu.my/id/eprint/27902/1/On%20solvability%20of%20some%20boundary%20value%20problems.pdf |