Proportional Itô–Doob Stochastic Fractional Order Systems
In this article, we discuss the existence and uniqueness of proportional Itô–Doob stochastic fractional order systems (PIDSFOS) by using the Picard iteration method. The paper provides new results using the proportional fractional integral and stochastic calculus techniques. We have shown the conver...
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| Format: | Article |
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MDPI AG
2023-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/9/2049 |
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| author | Abdellatif Ben Makhlouf Lassaad Mchiri Hakeem A. Othman Hafedh M. S. Rguigui Salah Boulaaras |
| author_facet | Abdellatif Ben Makhlouf Lassaad Mchiri Hakeem A. Othman Hafedh M. S. Rguigui Salah Boulaaras |
| author_sort | Abdellatif Ben Makhlouf |
| collection | DOAJ |
| description | In this article, we discuss the existence and uniqueness of proportional Itô–Doob stochastic fractional order systems (PIDSFOS) by using the Picard iteration method. The paper provides new results using the proportional fractional integral and stochastic calculus techniques. We have shown the convergence of the solution of the averaged PIDSFOS to that of the standard PIDSFOS in the context of the mean square and also in probability. One example is given to illustrate our results. |
| first_indexed | 2024-03-11T04:13:31Z |
| format | Article |
| id | doaj.art-c18f18c730444a8eb68dbef01f9f8e5f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T04:13:31Z |
| publishDate | 2023-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c18f18c730444a8eb68dbef01f9f8e5f2023-11-17T23:19:19ZengMDPI AGMathematics2227-73902023-04-01119204910.3390/math11092049Proportional Itô–Doob Stochastic Fractional Order SystemsAbdellatif Ben Makhlouf0Lassaad Mchiri1Hakeem A. Othman2Hafedh M. S. Rguigui3Salah Boulaaras4Department of Mathematics, College of Science, Jouf University, P.O. Box 2014, Sakaka 72388, Saudi ArabiaENSIIE, University of Evry-Val-d’Essonne, 1 Square de la Résistance, 91025 Évry-Courcouronnes, CEDEX, FranceDepartment of Mathematics, AL-Qunfudhah University College, Umm Al-Qura University, Al Qunfudhah 28821, Saudi ArabiaDepartment of Mathematics, AL-Qunfudhah University College, Umm Al-Qura University, Al Qunfudhah 28821, Saudi ArabiaDepartment of Mathematics, College of Sciences and Arts, ArRass, Qassim University, Almelida 51452, Saudi ArabiaIn this article, we discuss the existence and uniqueness of proportional Itô–Doob stochastic fractional order systems (PIDSFOS) by using the Picard iteration method. The paper provides new results using the proportional fractional integral and stochastic calculus techniques. We have shown the convergence of the solution of the averaged PIDSFOS to that of the standard PIDSFOS in the context of the mean square and also in probability. One example is given to illustrate our results.https://www.mdpi.com/2227-7390/11/9/2049stochastic systemproportional fractional integral |
| spellingShingle | Abdellatif Ben Makhlouf Lassaad Mchiri Hakeem A. Othman Hafedh M. S. Rguigui Salah Boulaaras Proportional Itô–Doob Stochastic Fractional Order Systems Mathematics stochastic system proportional fractional integral |
| title | Proportional Itô–Doob Stochastic Fractional Order Systems |
| title_full | Proportional Itô–Doob Stochastic Fractional Order Systems |
| title_fullStr | Proportional Itô–Doob Stochastic Fractional Order Systems |
| title_full_unstemmed | Proportional Itô–Doob Stochastic Fractional Order Systems |
| title_short | Proportional Itô–Doob Stochastic Fractional Order Systems |
| title_sort | proportional ito doob stochastic fractional order systems |
| topic | stochastic system proportional fractional integral |
| url | https://www.mdpi.com/2227-7390/11/9/2049 |
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