Boundary value problem with shift for one partial differential equation containing partial fractional derivative
We investigate a nonlocal boundary value problem for the equation of special type. For $y > 0$ it is the equation of fractional diffusion, which contains partial fractional derivative of Riemann-Liouville. For $y < 0$ it is the hyperbolic type equation with two perpendicular lines of degenerac...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2014-06-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
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| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/20719/16979 |
| _version_ | 1818059970103476224 |
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| author | Oleg A Repin |
| author_facet | Oleg A Repin |
| author_sort | Oleg A Repin |
| collection | DOAJ |
| description | We investigate a nonlocal boundary value problem for the equation of special type. For $y > 0$ it is the equation of fractional diffusion, which contains partial fractional derivative of Riemann-Liouville. For $y < 0$ it is the hyperbolic type equation with two perpendicular lines of degeneracy. The conditions of existence and uniqueness of the solution of the boundary value problem are formulated. The uniqueness of the solution of the problem is proved using the extremum principle and the use of generalized operator of fractional integro-differential in M. Saygo sense. The existence of a solution is reduced to the solvability of differential equations of fractional order, which solution is written out explicitly. |
| first_indexed | 2024-12-10T13:24:59Z |
| format | Article |
| id | doaj.art-f5ed8223af6b4adeba1129bb4dc7b846 |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-12-10T13:24:59Z |
| publishDate | 2014-06-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-f5ed8223af6b4adeba1129bb4dc7b8462022-12-22T01:47:13ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812014-06-01182223210.14498/vsgtu131818137Boundary value problem with shift for one partial differential equation containing partial fractional derivativeOleg A Repin0Samara State Economic UniversityWe investigate a nonlocal boundary value problem for the equation of special type. For $y > 0$ it is the equation of fractional diffusion, which contains partial fractional derivative of Riemann-Liouville. For $y < 0$ it is the hyperbolic type equation with two perpendicular lines of degeneracy. The conditions of existence and uniqueness of the solution of the boundary value problem are formulated. The uniqueness of the solution of the problem is proved using the extremum principle and the use of generalized operator of fractional integro-differential in M. Saygo sense. The existence of a solution is reduced to the solvability of differential equations of fractional order, which solution is written out explicitly.https://journals.eco-vector.com/1991-8615/article/viewFile/20719/16979boundary value problemgeneralized operator of fractional integrodifferentiationgauss hypergeometric functionmittag-leffer function |
| spellingShingle | Oleg A Repin Boundary value problem with shift for one partial differential equation containing partial fractional derivative Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki boundary value problem generalized operator of fractional integrodifferentiation gauss hypergeometric function mittag-leffer function |
| title | Boundary value problem with shift for one partial differential equation containing partial fractional derivative |
| title_full | Boundary value problem with shift for one partial differential equation containing partial fractional derivative |
| title_fullStr | Boundary value problem with shift for one partial differential equation containing partial fractional derivative |
| title_full_unstemmed | Boundary value problem with shift for one partial differential equation containing partial fractional derivative |
| title_short | Boundary value problem with shift for one partial differential equation containing partial fractional derivative |
| title_sort | boundary value problem with shift for one partial differential equation containing partial fractional derivative |
| topic | boundary value problem generalized operator of fractional integrodifferentiation gauss hypergeometric function mittag-leffer function |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/20719/16979 |
| work_keys_str_mv | AT olegarepin boundaryvalueproblemwithshiftforonepartialdifferentialequationcontainingpartialfractionalderivative |