Nonlocal problem for partial differential equations of fractional order
A nonlocal problem is investigated for the partial differential equation (diffusion equation of fractional order) in a finite domain. The boundary condition contains a linear combination of generalized operators of fractional integro-differentiation used on the solution in the characteristics and th...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2015-03-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| Subjects: | |
| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/20432/16679 |
| _version_ | 1818024567820517376 |
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| author | Oleg A Repin Anna V Tarasenko |
| author_facet | Oleg A Repin Anna V Tarasenko |
| author_sort | Oleg A Repin |
| collection | DOAJ |
| description | A nonlocal problem is investigated for the partial differential equation (diffusion equation of fractional order) in a finite domain. The boundary condition contains a linear combination of generalized operators of fractional integro-differentiation used on the solution in the characteristics and the solution and its derivative in the degenerating line. The uniqueness of the solution is proved by a modified Tricomi method. The existence of the solution is equivalently reduced to the question of the solvability of Fredholm integral equations of the second kind. |
| first_indexed | 2024-12-10T04:02:16Z |
| format | Article |
| id | doaj.art-58b093e053bc40c18fbb87b8347d8e98 |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-12-10T04:02:16Z |
| publishDate | 2015-03-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-58b093e053bc40c18fbb87b8347d8e982022-12-22T02:02:56ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812015-03-01191788610.14498/vsgtu139817852Nonlocal problem for partial differential equations of fractional orderOleg A Repin0Anna V Tarasenko1Samara State Economic UniversitySamara State University of Architecture and Civil EngineeringA nonlocal problem is investigated for the partial differential equation (diffusion equation of fractional order) in a finite domain. The boundary condition contains a linear combination of generalized operators of fractional integro-differentiation used on the solution in the characteristics and the solution and its derivative in the degenerating line. The uniqueness of the solution is proved by a modified Tricomi method. The existence of the solution is equivalently reduced to the question of the solvability of Fredholm integral equations of the second kind.https://journals.eco-vector.com/1991-8615/article/viewFile/20432/16679operator of fractional integro-differentiationboundary value problemfredholm integral equation of the second kind |
| spellingShingle | Oleg A Repin Anna V Tarasenko Nonlocal problem for partial differential equations of fractional order Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki operator of fractional integro-differentiation boundary value problem fredholm integral equation of the second kind |
| title | Nonlocal problem for partial differential equations of fractional order |
| title_full | Nonlocal problem for partial differential equations of fractional order |
| title_fullStr | Nonlocal problem for partial differential equations of fractional order |
| title_full_unstemmed | Nonlocal problem for partial differential equations of fractional order |
| title_short | Nonlocal problem for partial differential equations of fractional order |
| title_sort | nonlocal problem for partial differential equations of fractional order |
| topic | operator of fractional integro-differentiation boundary value problem fredholm integral equation of the second kind |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/20432/16679 |
| work_keys_str_mv | AT olegarepin nonlocalproblemforpartialdifferentialequationsoffractionalorder AT annavtarasenko nonlocalproblemforpartialdifferentialequationsoffractionalorder |