Hilfer-Katugampola fractional stochastic differential inclusions with Clarke sub-differential
The objective of this paper is to investigate the existence of mild solutions and optimal controls for a class of stochastic Hilfer-Katugampola fractional differential inclusions (SHKFDIs) with non-instantaneous impulsive (NIIs) that is strengthened by Brownian motion (BM) and the Clarke sub-differe...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2024-04-01
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| Series: | Heliyon |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2405844024056986 |
| _version_ | 1797200794898923520 |
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| author | Noorah Mshary Hamdy M. Ahmed Ahmed S. Ghanem A.M. Sayed Ahmed |
| author_facet | Noorah Mshary Hamdy M. Ahmed Ahmed S. Ghanem A.M. Sayed Ahmed |
| author_sort | Noorah Mshary |
| collection | DOAJ |
| description | The objective of this paper is to investigate the existence of mild solutions and optimal controls for a class of stochastic Hilfer-Katugampola fractional differential inclusions (SHKFDIs) with non-instantaneous impulsive (NIIs) that is strengthened by Brownian motion (BM) and the Clarke sub-differential. First, we establish a new set of sufficient conditions for the existence of mild solutions of the aforementioned fractional systems by using stochastic analysis, the Clarke sub-differential's characteristics, and the multi-valued fixed point theorem. Subsequently, by employing Balder's theorem, the existence of optimal control pairs for the considered system is investigated. Eventually, an example is provided to validate the obtained results. |
| first_indexed | 2024-04-24T07:37:19Z |
| format | Article |
| id | doaj.art-575d745c9ca540288a4e795866d90cb6 |
| institution | Directory Open Access Journal |
| issn | 2405-8440 |
| language | English |
| last_indexed | 2024-04-24T07:37:19Z |
| publishDate | 2024-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Heliyon |
| spelling | doaj.art-575d745c9ca540288a4e795866d90cb62024-04-20T04:17:39ZengElsevierHeliyon2405-84402024-04-01108e29667Hilfer-Katugampola fractional stochastic differential inclusions with Clarke sub-differentialNoorah Mshary0Hamdy M. Ahmed1Ahmed S. Ghanem2A.M. Sayed Ahmed3Department of Mathematics, College of Science, Jazan University, P.O. Box. 114, Jazan 45142, Kingdom of Saudi ArabiaDepartment of Physics and Engineering Mathematics, Higher Institute of Engineering, El-Shorouk Academy, El-Shorouk City, Cairo, Egypt; Corresponding author.Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El-Shorouk Academy, El-Shorouk City, Cairo, EgyptDepartment of mathematics and computer Science, Faculty of Science, Alexandria university, Alexandria, EgyptThe objective of this paper is to investigate the existence of mild solutions and optimal controls for a class of stochastic Hilfer-Katugampola fractional differential inclusions (SHKFDIs) with non-instantaneous impulsive (NIIs) that is strengthened by Brownian motion (BM) and the Clarke sub-differential. First, we establish a new set of sufficient conditions for the existence of mild solutions of the aforementioned fractional systems by using stochastic analysis, the Clarke sub-differential's characteristics, and the multi-valued fixed point theorem. Subsequently, by employing Balder's theorem, the existence of optimal control pairs for the considered system is investigated. Eventually, an example is provided to validate the obtained results.http://www.sciencedirect.com/science/article/pii/S2405844024056986Hilfer-Katugampola fractional derivativeOptimal controlStochastic differential inclusionsMeasure of non-compactnessBalder's theorem |
| spellingShingle | Noorah Mshary Hamdy M. Ahmed Ahmed S. Ghanem A.M. Sayed Ahmed Hilfer-Katugampola fractional stochastic differential inclusions with Clarke sub-differential Heliyon Hilfer-Katugampola fractional derivative Optimal control Stochastic differential inclusions Measure of non-compactness Balder's theorem |
| title | Hilfer-Katugampola fractional stochastic differential inclusions with Clarke sub-differential |
| title_full | Hilfer-Katugampola fractional stochastic differential inclusions with Clarke sub-differential |
| title_fullStr | Hilfer-Katugampola fractional stochastic differential inclusions with Clarke sub-differential |
| title_full_unstemmed | Hilfer-Katugampola fractional stochastic differential inclusions with Clarke sub-differential |
| title_short | Hilfer-Katugampola fractional stochastic differential inclusions with Clarke sub-differential |
| title_sort | hilfer katugampola fractional stochastic differential inclusions with clarke sub differential |
| topic | Hilfer-Katugampola fractional derivative Optimal control Stochastic differential inclusions Measure of non-compactness Balder's theorem |
| url | http://www.sciencedirect.com/science/article/pii/S2405844024056986 |
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