Monotone iterative technique for periodic problem involving Riemann–Liouville fractional derivatives in Banach spaces
Abstract In this paper, we use a monotone iterative technique in the presence of lower and upper solutions to discuss the existence and uniqueness of periodic solutions for a class of fractional differential equations in an ordered Banach space E. Under some monotonicity conditions and noncompactnes...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-07-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-018-1037-4 |
| _version_ | 1818027200896565248 |
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| author | Yonghong Ding Yongxiang Li |
| author_facet | Yonghong Ding Yongxiang Li |
| author_sort | Yonghong Ding |
| collection | DOAJ |
| description | Abstract In this paper, we use a monotone iterative technique in the presence of lower and upper solutions to discuss the existence and uniqueness of periodic solutions for a class of fractional differential equations in an ordered Banach space E. Under some monotonicity conditions and noncompactness measure conditions of nonlinearity, we obtain the existence of extremal solutions and a unique solution between lower and upper solutions. |
| first_indexed | 2024-12-10T04:44:08Z |
| format | Article |
| id | doaj.art-5c67023406b8414fb50cdacd3e4141e2 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-10T04:44:08Z |
| publishDate | 2018-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-5c67023406b8414fb50cdacd3e4141e22022-12-22T02:01:48ZengSpringerOpenBoundary Value Problems1687-27702018-07-012018111410.1186/s13661-018-1037-4Monotone iterative technique for periodic problem involving Riemann–Liouville fractional derivatives in Banach spacesYonghong Ding0Yongxiang Li1Department of Mathematics, Northwest Normal UniversityDepartment of Mathematics, Northwest Normal UniversityAbstract In this paper, we use a monotone iterative technique in the presence of lower and upper solutions to discuss the existence and uniqueness of periodic solutions for a class of fractional differential equations in an ordered Banach space E. Under some monotonicity conditions and noncompactness measure conditions of nonlinearity, we obtain the existence of extremal solutions and a unique solution between lower and upper solutions.http://link.springer.com/article/10.1186/s13661-018-1037-4Monotone iterative techniqueLower and upper solutionsConeFractional differential equationsMeasure of noncompactness |
| spellingShingle | Yonghong Ding Yongxiang Li Monotone iterative technique for periodic problem involving Riemann–Liouville fractional derivatives in Banach spaces Boundary Value Problems Monotone iterative technique Lower and upper solutions Cone Fractional differential equations Measure of noncompactness |
| title | Monotone iterative technique for periodic problem involving Riemann–Liouville fractional derivatives in Banach spaces |
| title_full | Monotone iterative technique for periodic problem involving Riemann–Liouville fractional derivatives in Banach spaces |
| title_fullStr | Monotone iterative technique for periodic problem involving Riemann–Liouville fractional derivatives in Banach spaces |
| title_full_unstemmed | Monotone iterative technique for periodic problem involving Riemann–Liouville fractional derivatives in Banach spaces |
| title_short | Monotone iterative technique for periodic problem involving Riemann–Liouville fractional derivatives in Banach spaces |
| title_sort | monotone iterative technique for periodic problem involving riemann liouville fractional derivatives in banach spaces |
| topic | Monotone iterative technique Lower and upper solutions Cone Fractional differential equations Measure of noncompactness |
| url | http://link.springer.com/article/10.1186/s13661-018-1037-4 |
| work_keys_str_mv | AT yonghongding monotoneiterativetechniqueforperiodicprobleminvolvingriemannliouvillefractionalderivativesinbanachspaces AT yongxiangli monotoneiterativetechniqueforperiodicprobleminvolvingriemannliouvillefractionalderivativesinbanachspaces |