A Study on Controllability of a Class of Impulsive Fractional Nonlinear Evolution Equations with Delay in Banach Spaces
Under a new generalized definition of exact controllability we introduced and with a appropriately constructed time delay term in a special complete space to overcome the delay-induced-difficulty, we establish the sufficient conditions of the exact controllability for a class of impulsive fractional...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/5/4/279 |
| _version_ | 1797504496231776256 |
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| author | Daliang Zhao |
| author_facet | Daliang Zhao |
| author_sort | Daliang Zhao |
| collection | DOAJ |
| description | Under a new generalized definition of exact controllability we introduced and with a appropriately constructed time delay term in a special complete space to overcome the delay-induced-difficulty, we establish the sufficient conditions of the exact controllability for a class of impulsive fractional nonlinear evolution equations with delay by using the resolvent operator theory and the theory of nonlinear functional analysis. Nonlinearity in the system is only supposed to be continuous rather than Lipschitz continuous by contrast. The results obtained in the present work are generalizations and continuations of the recent results on this issue. Further, an example is presented to show the effectiveness of the new results. |
| first_indexed | 2024-03-10T04:05:24Z |
| format | Article |
| id | doaj.art-7267ffd77ac34d8487bee4bc1ee02f9e |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T04:05:24Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-7267ffd77ac34d8487bee4bc1ee02f9e2023-11-23T08:24:45ZengMDPI AGFractal and Fractional2504-31102021-12-015427910.3390/fractalfract5040279A Study on Controllability of a Class of Impulsive Fractional Nonlinear Evolution Equations with Delay in Banach SpacesDaliang Zhao0School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, ChinaUnder a new generalized definition of exact controllability we introduced and with a appropriately constructed time delay term in a special complete space to overcome the delay-induced-difficulty, we establish the sufficient conditions of the exact controllability for a class of impulsive fractional nonlinear evolution equations with delay by using the resolvent operator theory and the theory of nonlinear functional analysis. Nonlinearity in the system is only supposed to be continuous rather than Lipschitz continuous by contrast. The results obtained in the present work are generalizations and continuations of the recent results on this issue. Further, an example is presented to show the effectiveness of the new results.https://www.mdpi.com/2504-3110/5/4/279controllabilityimpulsive fractional evolution equationsdelaymeasure of noncompactnessmild solutionfixed point theorem |
| spellingShingle | Daliang Zhao A Study on Controllability of a Class of Impulsive Fractional Nonlinear Evolution Equations with Delay in Banach Spaces Fractal and Fractional controllability impulsive fractional evolution equations delay measure of noncompactness mild solution fixed point theorem |
| title | A Study on Controllability of a Class of Impulsive Fractional Nonlinear Evolution Equations with Delay in Banach Spaces |
| title_full | A Study on Controllability of a Class of Impulsive Fractional Nonlinear Evolution Equations with Delay in Banach Spaces |
| title_fullStr | A Study on Controllability of a Class of Impulsive Fractional Nonlinear Evolution Equations with Delay in Banach Spaces |
| title_full_unstemmed | A Study on Controllability of a Class of Impulsive Fractional Nonlinear Evolution Equations with Delay in Banach Spaces |
| title_short | A Study on Controllability of a Class of Impulsive Fractional Nonlinear Evolution Equations with Delay in Banach Spaces |
| title_sort | study on controllability of a class of impulsive fractional nonlinear evolution equations with delay in banach spaces |
| topic | controllability impulsive fractional evolution equations delay measure of noncompactness mild solution fixed point theorem |
| url | https://www.mdpi.com/2504-3110/5/4/279 |
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