Existence and controllability of nonlinear evolution equation involving Hilfer fractional derivative with noise and impulsive effect via Rosenblatt process and Poisson jumps
This manuscript explores a new class of Hilfer fractional stochastic differential system, as driven by the Wiener process and Rosenblatt process through the application of non-instantaneous impulsive effects and Poisson jumps. Existence of a mild solution to the considered system is proved. Sufficie...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://aimspress.com/article/doi/10.3934/math.2024477?viewType=HTML |
| _version_ | 1797254106651295744 |
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| author | Noorah Mshary Hamdy M. Ahmed Ahmed S. Ghanem |
| author_facet | Noorah Mshary Hamdy M. Ahmed Ahmed S. Ghanem |
| author_sort | Noorah Mshary |
| collection | DOAJ |
| description | This manuscript explores a new class of Hilfer fractional stochastic differential system, as driven by the Wiener process and Rosenblatt process through the application of non-instantaneous impulsive effects and Poisson jumps. Existence of a mild solution to the considered system is proved. Sufficient conditions for the controllability of the proposed control system are established. To prove our main results, we utilize fractional calculus, stochastic analysis, semigroup theory, and the Sadovskii fixed point theorem. In addition, to illustrate the theoretical findings, we present an example. |
| first_indexed | 2024-04-24T21:44:41Z |
| format | Article |
| id | doaj.art-669ae570180549f0b9a05a51ed89922d |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-24T21:44:41Z |
| publishDate | 2024-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-669ae570180549f0b9a05a51ed89922d2024-03-21T01:31:50ZengAIMS PressAIMS Mathematics2473-69882024-03-01949746976910.3934/math.2024477Existence and controllability of nonlinear evolution equation involving Hilfer fractional derivative with noise and impulsive effect via Rosenblatt process and Poisson jumpsNoorah Mshary0Hamdy M. Ahmed1Ahmed S. Ghanem21. Department of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi Arabia2. Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El-Shorouk Academy, El-Shorouk City, Cairo, Egypt2. Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El-Shorouk Academy, El-Shorouk City, Cairo, EgyptThis manuscript explores a new class of Hilfer fractional stochastic differential system, as driven by the Wiener process and Rosenblatt process through the application of non-instantaneous impulsive effects and Poisson jumps. Existence of a mild solution to the considered system is proved. Sufficient conditions for the controllability of the proposed control system are established. To prove our main results, we utilize fractional calculus, stochastic analysis, semigroup theory, and the Sadovskii fixed point theorem. In addition, to illustrate the theoretical findings, we present an example.https://aimspress.com/article/doi/10.3934/math.2024477?viewType=HTMLimpulsive effectfractional calculusstochastic differential systemcontrol theorysemigroup theory |
| spellingShingle | Noorah Mshary Hamdy M. Ahmed Ahmed S. Ghanem Existence and controllability of nonlinear evolution equation involving Hilfer fractional derivative with noise and impulsive effect via Rosenblatt process and Poisson jumps AIMS Mathematics impulsive effect fractional calculus stochastic differential system control theory semigroup theory |
| title | Existence and controllability of nonlinear evolution equation involving Hilfer fractional derivative with noise and impulsive effect via Rosenblatt process and Poisson jumps |
| title_full | Existence and controllability of nonlinear evolution equation involving Hilfer fractional derivative with noise and impulsive effect via Rosenblatt process and Poisson jumps |
| title_fullStr | Existence and controllability of nonlinear evolution equation involving Hilfer fractional derivative with noise and impulsive effect via Rosenblatt process and Poisson jumps |
| title_full_unstemmed | Existence and controllability of nonlinear evolution equation involving Hilfer fractional derivative with noise and impulsive effect via Rosenblatt process and Poisson jumps |
| title_short | Existence and controllability of nonlinear evolution equation involving Hilfer fractional derivative with noise and impulsive effect via Rosenblatt process and Poisson jumps |
| title_sort | existence and controllability of nonlinear evolution equation involving hilfer fractional derivative with noise and impulsive effect via rosenblatt process and poisson jumps |
| topic | impulsive effect fractional calculus stochastic differential system control theory semigroup theory |
| url | https://aimspress.com/article/doi/10.3934/math.2024477?viewType=HTML |
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