Controllability results to non-instantaneous impulsive with infinite delay for generalized fractional differential equations
This paper discusses controllability results for active types with infinite-time delay of non-instantaneous impulsive fractional differential equations. The model is constructed based on the generalized Caputo (Caputo-Katugampola) fractional derivative and the control function with non-local Katugam...
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| Format: | Article |
| Language: | English |
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Elsevier
2023-05-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016823001588 |
| _version_ | 1797833154044624896 |
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| author | Ahmed Salem Sanaa Abdullah |
| author_facet | Ahmed Salem Sanaa Abdullah |
| author_sort | Ahmed Salem |
| collection | DOAJ |
| description | This paper discusses controllability results for active types with infinite-time delay of non-instantaneous impulsive fractional differential equations. The model is constructed based on the generalized Caputo (Caputo-Katugampola) fractional derivative and the control function with non-local Katugampola fractional integral as a boundary condition. Our principal results are established by giving some sufficient hypotheses, utilizing well-known fractional calculus truths and using Krasnoselskii’s fixed point theorem. The infinite time delay has been treated with the abstract phase space techniques and fulfilling the ensuing axioms due to Hale and Kato. It turns out that under some sufficient conditions, the problem has at least one controllable solution. An implementation of our theoretical results is demonstrated by a numerical example. |
| first_indexed | 2024-04-09T14:19:59Z |
| format | Article |
| id | doaj.art-ca1c4800d2e548bd9b65b84a5c8b1df4 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-04-09T14:19:59Z |
| publishDate | 2023-05-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-ca1c4800d2e548bd9b65b84a5c8b1df42023-05-05T04:40:01ZengElsevierAlexandria Engineering Journal1110-01682023-05-0170525533Controllability results to non-instantaneous impulsive with infinite delay for generalized fractional differential equationsAhmed Salem0Sanaa Abdullah1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O.Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P.O.Box 80203, Jeddah 21589, Saudi ArabiaThis paper discusses controllability results for active types with infinite-time delay of non-instantaneous impulsive fractional differential equations. The model is constructed based on the generalized Caputo (Caputo-Katugampola) fractional derivative and the control function with non-local Katugampola fractional integral as a boundary condition. Our principal results are established by giving some sufficient hypotheses, utilizing well-known fractional calculus truths and using Krasnoselskii’s fixed point theorem. The infinite time delay has been treated with the abstract phase space techniques and fulfilling the ensuing axioms due to Hale and Kato. It turns out that under some sufficient conditions, the problem has at least one controllable solution. An implementation of our theoretical results is demonstrated by a numerical example.http://www.sciencedirect.com/science/article/pii/S1110016823001588Non-instantaneous impulsesControllabilityInfinite time-delayGeneralized Liouville-Caputo derivativeFixed point theorem |
| spellingShingle | Ahmed Salem Sanaa Abdullah Controllability results to non-instantaneous impulsive with infinite delay for generalized fractional differential equations Alexandria Engineering Journal Non-instantaneous impulses Controllability Infinite time-delay Generalized Liouville-Caputo derivative Fixed point theorem |
| title | Controllability results to non-instantaneous impulsive with infinite delay for generalized fractional differential equations |
| title_full | Controllability results to non-instantaneous impulsive with infinite delay for generalized fractional differential equations |
| title_fullStr | Controllability results to non-instantaneous impulsive with infinite delay for generalized fractional differential equations |
| title_full_unstemmed | Controllability results to non-instantaneous impulsive with infinite delay for generalized fractional differential equations |
| title_short | Controllability results to non-instantaneous impulsive with infinite delay for generalized fractional differential equations |
| title_sort | controllability results to non instantaneous impulsive with infinite delay for generalized fractional differential equations |
| topic | Non-instantaneous impulses Controllability Infinite time-delay Generalized Liouville-Caputo derivative Fixed point theorem |
| url | http://www.sciencedirect.com/science/article/pii/S1110016823001588 |
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