A study on controllability of impulsive fractional evolution equations via resolvent operators
Abstract In this article, we study the controllability for impulsive fractional integro-differential evolution equation in a Banach space. The discussions are based on the Mönch fixed point theorem as well as the theory of fractional calculus and the ( α , β ) $(\alpha ,\beta )$ -resolvent operator,...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-02-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-021-01499-5 |
| _version_ | 1818914841260195840 |
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| author | Haide Gou Yongxiang Li |
| author_facet | Haide Gou Yongxiang Li |
| author_sort | Haide Gou |
| collection | DOAJ |
| description | Abstract In this article, we study the controllability for impulsive fractional integro-differential evolution equation in a Banach space. The discussions are based on the Mönch fixed point theorem as well as the theory of fractional calculus and the ( α , β ) $(\alpha ,\beta )$ -resolvent operator, we concern with the term u ′ ( ⋅ ) $u'(\cdot )$ and finding a control v such that the mild solution satisfies u ( b ) = u b $u(b)=u_{b}$ and u ′ ( b ) = u b ′ $u'(b)=u'_{b}$ . Finally, we present an application to support the validity study. |
| first_indexed | 2024-12-19T23:52:47Z |
| format | Article |
| id | doaj.art-f533b017955940cc96f5dd1da6314a39 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-19T23:52:47Z |
| publishDate | 2021-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-f533b017955940cc96f5dd1da6314a392022-12-21T20:01:06ZengSpringerOpenBoundary Value Problems1687-27702021-02-012021112210.1186/s13661-021-01499-5A study on controllability of impulsive fractional evolution equations via resolvent operatorsHaide Gou0Yongxiang Li1Department of Mathematics, Northwest Normal UniversityDepartment of Mathematics, Northwest Normal UniversityAbstract In this article, we study the controllability for impulsive fractional integro-differential evolution equation in a Banach space. The discussions are based on the Mönch fixed point theorem as well as the theory of fractional calculus and the ( α , β ) $(\alpha ,\beta )$ -resolvent operator, we concern with the term u ′ ( ⋅ ) $u'(\cdot )$ and finding a control v such that the mild solution satisfies u ( b ) = u b $u(b)=u_{b}$ and u ′ ( b ) = u b ′ $u'(b)=u'_{b}$ . Finally, we present an application to support the validity study.https://doi.org/10.1186/s13661-021-01499-5ControllabilityMeasure of noncompactnessMild solutionMönch fixed point theorem |
| spellingShingle | Haide Gou Yongxiang Li A study on controllability of impulsive fractional evolution equations via resolvent operators Boundary Value Problems Controllability Measure of noncompactness Mild solution Mönch fixed point theorem |
| title | A study on controllability of impulsive fractional evolution equations via resolvent operators |
| title_full | A study on controllability of impulsive fractional evolution equations via resolvent operators |
| title_fullStr | A study on controllability of impulsive fractional evolution equations via resolvent operators |
| title_full_unstemmed | A study on controllability of impulsive fractional evolution equations via resolvent operators |
| title_short | A study on controllability of impulsive fractional evolution equations via resolvent operators |
| title_sort | study on controllability of impulsive fractional evolution equations via resolvent operators |
| topic | Controllability Measure of noncompactness Mild solution Mönch fixed point theorem |
| url | https://doi.org/10.1186/s13661-021-01499-5 |
| work_keys_str_mv | AT haidegou astudyoncontrollabilityofimpulsivefractionalevolutionequationsviaresolventoperators AT yongxiangli astudyoncontrollabilityofimpulsivefractionalevolutionequationsviaresolventoperators AT haidegou studyoncontrollabilityofimpulsivefractionalevolutionequationsviaresolventoperators AT yongxiangli studyoncontrollabilityofimpulsivefractionalevolutionequationsviaresolventoperators |