Generalized boundary value problem for a linear ordinary differential equation with a discretely distributed fractional differentiation operator
This paper formulates and solves a generalized boundary value problem for a linear ordinary differential equation with a discretely distributed fractional differentiation operator. The fractional derivative is understood as the Gerasimov-Caputo derivative. The boundary conditions are given in the f...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2022-06-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
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| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/503 |
| _version_ | 1827395732588462080 |
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| author | L.Kh. Gadzova |
| author_facet | L.Kh. Gadzova |
| author_sort | L.Kh. Gadzova |
| collection | DOAJ |
| description |
This paper formulates and solves a generalized boundary value problem for a linear ordinary differential equation with a discretely distributed fractional differentiation operator. The fractional derivative is understood as the Gerasimov-Caputo derivative. The boundary conditions are given in the form of linear functionals, which makes it possible to cover a wide class of linear local and non-local conditions. A representation of the solution is found in terms of special functions. A necessary and sufficient condition for the solvability of the problem under study is obtained, as well as conditions under which the solvability condition is certainly satisfied. The theorem of existence and uniqueness of the solution is proved.
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| first_indexed | 2024-03-08T18:39:01Z |
| format | Article |
| id | doaj.art-784aa40667fc448e83623f271fc6f063 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:39:01Z |
| publishDate | 2022-06-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-784aa40667fc448e83623f271fc6f0632023-12-29T10:19:24ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112022-06-01106210.31489/2022m2/108-116Generalized boundary value problem for a linear ordinary differential equation with a discretely distributed fractional differentiation operatorL.Kh. Gadzova This paper formulates and solves a generalized boundary value problem for a linear ordinary differential equation with a discretely distributed fractional differentiation operator. The fractional derivative is understood as the Gerasimov-Caputo derivative. The boundary conditions are given in the form of linear functionals, which makes it possible to cover a wide class of linear local and non-local conditions. A representation of the solution is found in terms of special functions. A necessary and sufficient condition for the solvability of the problem under study is obtained, as well as conditions under which the solvability condition is certainly satisfied. The theorem of existence and uniqueness of the solution is proved. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/503fractional differentiation operatorCaputo derivativeboundary value problemfunctionalWright function |
| spellingShingle | L.Kh. Gadzova Generalized boundary value problem for a linear ordinary differential equation with a discretely distributed fractional differentiation operator Қарағанды университетінің хабаршысы. Математика сериясы fractional differentiation operator Caputo derivative boundary value problem functional Wright function |
| title | Generalized boundary value problem for a linear ordinary differential equation with a discretely distributed fractional differentiation operator |
| title_full | Generalized boundary value problem for a linear ordinary differential equation with a discretely distributed fractional differentiation operator |
| title_fullStr | Generalized boundary value problem for a linear ordinary differential equation with a discretely distributed fractional differentiation operator |
| title_full_unstemmed | Generalized boundary value problem for a linear ordinary differential equation with a discretely distributed fractional differentiation operator |
| title_short | Generalized boundary value problem for a linear ordinary differential equation with a discretely distributed fractional differentiation operator |
| title_sort | generalized boundary value problem for a linear ordinary differential equation with a discretely distributed fractional differentiation operator |
| topic | fractional differentiation operator Caputo derivative boundary value problem functional Wright function |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/503 |
| work_keys_str_mv | AT lkhgadzova generalizedboundaryvalueproblemforalinearordinarydifferentialequationwithadiscretelydistributedfractionaldifferentiationoperator |