Integro-differential equations with bounded operators in Banach spaces
The paper investigates integro-differential equations in Banach spaces with operators, which are a composition of convolution and differentiation operators. Depending on the order of action of these two operators, we talk about integro-differential operators of the Riemann—Liouville type, w...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Academician Ye.A. Buketov Karaganda University
2022-06-01
|
| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
| Online Access: | https://mathematics-vestnik.ksu.kz/apart/2022-106-2/8.pdf |
| _version_ | 1797687127168778240 |
|---|---|
| author | V.E. Fedorov A.D. Godova B.T. Kien |
| author_facet | V.E. Fedorov A.D. Godova B.T. Kien |
| author_sort | V.E. Fedorov |
| collection | DOAJ |
| description | The paper investigates integro-differential equations in Banach spaces with operators, which are a composition of convolution and differentiation operators. Depending on the order of action of these two operators, we talk about integro-differential operators of the Riemann—Liouville type, when the convolution operator acts first, and integro-differential operators of the Gerasimov type otherwise. Special cases of the operators under consideration are the fractional derivatives of Riemann—Liouville and Gerasimov, respectively. The classes of integro-differential operators under study also include those in which the convolution has an integral kernel without singularities. The conditions of the unique solvability of the Cauchy type problem for a linear integro-differential equation of the Riemann—Liouville type and the Cauchy problem for a linear integrodifferential equation of the Gerasimov type with a bounded operator at the unknown function are obtained. These results are used in the study of similar equations with a degenerate operator at an integro-differential operator under the condition of relative boundedness of the pair of operators from the equation. Abstract results are applied to the study of initial boundary value problems for partial differential equations with an integro-differential operator, the convolution in which is given by the Mittag-Leffler function multiplied by a power function. |
| first_indexed | 2024-03-12T01:14:46Z |
| format | Article |
| id | doaj.art-7cc05f79e6bb4d31bc339adabf09d135 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-12T01:14:46Z |
| publishDate | 2022-06-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-7cc05f79e6bb4d31bc339adabf09d1352023-09-13T18:31:36ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112022-06-0110629310710.31489/2022M2/93-107Integro-differential equations with bounded operators in Banach spacesV.E. FedorovA.D. GodovaB.T. Kien The paper investigates integro-differential equations in Banach spaces with operators, which are a composition of convolution and differentiation operators. Depending on the order of action of these two operators, we talk about integro-differential operators of the Riemann—Liouville type, when the convolution operator acts first, and integro-differential operators of the Gerasimov type otherwise. Special cases of the operators under consideration are the fractional derivatives of Riemann—Liouville and Gerasimov, respectively. The classes of integro-differential operators under study also include those in which the convolution has an integral kernel without singularities. The conditions of the unique solvability of the Cauchy type problem for a linear integro-differential equation of the Riemann—Liouville type and the Cauchy problem for a linear integrodifferential equation of the Gerasimov type with a bounded operator at the unknown function are obtained. These results are used in the study of similar equations with a degenerate operator at an integro-differential operator under the condition of relative boundedness of the pair of operators from the equation. Abstract results are applied to the study of initial boundary value problems for partial differential equations with an integro-differential operator, the convolution in which is given by the Mittag-Leffler function multiplied by a power function.https://mathematics-vestnik.ksu.kz/apart/2022-106-2/8.pdf |
| spellingShingle | V.E. Fedorov A.D. Godova B.T. Kien Integro-differential equations with bounded operators in Banach spaces Қарағанды университетінің хабаршысы. Математика сериясы |
| title | Integro-differential equations with bounded operators in Banach spaces |
| title_full | Integro-differential equations with bounded operators in Banach spaces |
| title_fullStr | Integro-differential equations with bounded operators in Banach spaces |
| title_full_unstemmed | Integro-differential equations with bounded operators in Banach spaces |
| title_short | Integro-differential equations with bounded operators in Banach spaces |
| title_sort | integro differential equations with bounded operators in banach spaces |
| url | https://mathematics-vestnik.ksu.kz/apart/2022-106-2/8.pdf |
| work_keys_str_mv | AT vefedorov integrodifferentialequationswithboundedoperatorsinbanachspaces AT adgodova integrodifferentialequationswithboundedoperatorsinbanachspaces AT btkien integrodifferentialequationswithboundedoperatorsinbanachspaces |