Boundary value problem for fractional diffusion equation in a curvilinear angle domain
We consider a boundary value problem for the fractional diffusion equation in an angle domain with a curvilinear boundary. Existence and uniqueness theorems for solutions are proved. It is shown that Holder continuity of the curvilinear boundary ensures the existence of solutions. The uniqu...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2022-03-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Online Access: | https://mathematics-vestnik.ksu.kz/apart/2022-105-1/9.pdf |
| _version_ | 1797687147213357056 |
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| author | A.V. Pskhu M.I. Ramazanov N.K. Gulmanov S.A. Iskakov |
| author_facet | A.V. Pskhu M.I. Ramazanov N.K. Gulmanov S.A. Iskakov |
| author_sort | A.V. Pskhu |
| collection | DOAJ |
| description | We consider a boundary value problem for the fractional diffusion equation in an angle domain with a curvilinear boundary. Existence and uniqueness theorems for solutions are proved. It is shown that Holder continuity of the curvilinear boundary ensures the existence of solutions. The uniqueness is proved in the class of functions that vanish at infinity with a power weight. The solution to the problem is constructed explicitly in terms of the solution of the Volterra integral equation. |
| first_indexed | 2024-03-12T01:15:05Z |
| format | Article |
| id | doaj.art-d4a76bff55b441b69d6244f36205989b |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-12T01:15:05Z |
| publishDate | 2022-03-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-d4a76bff55b441b69d6244f36205989b2023-09-13T18:31:25ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112022-03-011051839510.31489/2022M1/83-95Boundary value problem for fractional diffusion equation in a curvilinear angle domainA.V. PskhuM.I. RamazanovN.K. Gulmanov S.A. Iskakov We consider a boundary value problem for the fractional diffusion equation in an angle domain with a curvilinear boundary. Existence and uniqueness theorems for solutions are proved. It is shown that Holder continuity of the curvilinear boundary ensures the existence of solutions. The uniqueness is proved in the class of functions that vanish at infinity with a power weight. The solution to the problem is constructed explicitly in terms of the solution of the Volterra integral equation.https://mathematics-vestnik.ksu.kz/apart/2022-105-1/9.pdf |
| spellingShingle | A.V. Pskhu M.I. Ramazanov N.K. Gulmanov S.A. Iskakov Boundary value problem for fractional diffusion equation in a curvilinear angle domain Қарағанды университетінің хабаршысы. Математика сериясы |
| title | Boundary value problem for fractional diffusion equation in a curvilinear angle domain |
| title_full | Boundary value problem for fractional diffusion equation in a curvilinear angle domain |
| title_fullStr | Boundary value problem for fractional diffusion equation in a curvilinear angle domain |
| title_full_unstemmed | Boundary value problem for fractional diffusion equation in a curvilinear angle domain |
| title_short | Boundary value problem for fractional diffusion equation in a curvilinear angle domain |
| title_sort | boundary value problem for fractional diffusion equation in a curvilinear angle domain |
| url | https://mathematics-vestnik.ksu.kz/apart/2022-105-1/9.pdf |
| work_keys_str_mv | AT avpskhu boundaryvalueproblemforfractionaldiffusionequationinacurvilinearangledomain AT miramazanov boundaryvalueproblemforfractionaldiffusionequationinacurvilinearangledomain AT nkgulmanov boundaryvalueproblemforfractionaldiffusionequationinacurvilinearangledomain AT saiskakov boundaryvalueproblemforfractionaldiffusionequationinacurvilinearangledomain |