On the existence of solutions for a differential inclusion of fractional order with upper-semicontinuous right-hand side
We prove a theorem on the existence of solutions of the differential inclusion \(D_0^\alpha u(x) \in F(x,u(x)), u_{1 - \alpha } (0) = \gamma , \left( {u_{1 - \alpha } (x) = 1_0^{1 - \alpha } u(x)} \right),\) where \(\alpha \in (0,1), D_0^\alpha u(x) \left( {1_0^{1 - \alpha } u(x)} \right)\) is...
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| Дата: | 1999 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | Українська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1999
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/4757 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510924297732096 |
|---|---|
| author | Vityuk, A. N. Вітюк, А. Н. |
| author_facet | Vityuk, A. N. Вітюк, А. Н. |
| author_sort | Vityuk, A. N. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:13:14Z |
| description | We prove a theorem on the existence of solutions of the differential inclusion \(D_0^\alpha u(x) \in F(x,u(x)), u_{1 - \alpha } (0) = \gamma , \left( {u_{1 - \alpha } (x) = 1_0^{1 - \alpha } u(x)} \right),\) where \(\alpha \in (0,1), D_0^\alpha u(x) \left( {1_0^{1 - \alpha } u(x)} \right)\) is the Riemann-Liouville derivative (integral) of order α, and the multivalued mappingF(x, u) is upper semicontinuous inu. |
| first_indexed | 2026-03-24T03:04:43Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4757 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:04:43Z |
| publishDate | 1999 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/0c/c1c06568d432a001c43777c991bf1e0c.pdf |
| spelling | umjimathkievua-article-47572020-03-18T21:13:14Z On the existence of solutions for a differential inclusion of fractional order with upper-semicontinuous right-hand side Существование решений дифференциального включения дробного порядка с полунепрерывной сверху правой частью Vityuk, A. N. Вітюк, А. Н. We prove a theorem on the existence of solutions of the differential inclusion \(D_0^\alpha u(x) \in F(x,u(x)), u_{1 - \alpha } (0) = \gamma , \left( {u_{1 - \alpha } (x) = 1_0^{1 - \alpha } u(x)} \right),\) where \(\alpha \in (0,1), D_0^\alpha u(x) \left( {1_0^{1 - \alpha } u(x)} \right)\) is the Riemann-Liouville derivative (integral) of order α, and the multivalued mappingF(x, u) is upper semicontinuous inu. Доведено теорему про існування розв'язків диференціального включення $D_0^\alpha u(x) \in F(x,u(x)), u_{1 - \alpha } (0) = \gamma , \left( {u_{1 - \alpha } (x) = 1_0^{1 - \alpha } u(x)} \right),$ де $\alpha \in (0,1), D_0^\alpha u(x) \left( {1_0^{1 - \alpha } u(x)} \right)$—похідна (інтеграл) Рімана - Ліувілля порядку $α$, а многозначне відображення $F(x, u)$ напівнеперервне зверху по $u$. Institute of Mathematics, NAS of Ukraine 1999-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4757 Ukrains’kyi Matematychnyi Zhurnal; Vol. 51 No. 11 (1999); 1562–1565 Український математичний журнал; Том 51 № 11 (1999); 1562–1565 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4757/6215 https://umj.imath.kiev.ua/index.php/umj/article/view/4757/6216 Copyright (c) 1999 Vityuk A. N. |
| spellingShingle | Vityuk, A. N. Вітюк, А. Н. On the existence of solutions for a differential inclusion of fractional order with upper-semicontinuous right-hand side |
| title | On the existence of solutions for a differential inclusion of fractional order with upper-semicontinuous right-hand side |
| title_alt | Существование решений дифференциального включения дробного порядка с полунепрерывной сверху правой частью |
| title_full | On the existence of solutions for a differential inclusion of fractional order with upper-semicontinuous right-hand side |
| title_fullStr | On the existence of solutions for a differential inclusion of fractional order with upper-semicontinuous right-hand side |
| title_full_unstemmed | On the existence of solutions for a differential inclusion of fractional order with upper-semicontinuous right-hand side |
| title_short | On the existence of solutions for a differential inclusion of fractional order with upper-semicontinuous right-hand side |
| title_sort | on the existence of solutions for a differential inclusion of fractional order with upper-semicontinuous right-hand side |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4757 |
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