On the Existence and Stability of a Neutral Stochastic Fractional Differential System
The main purpose of this paper is to investigate the existence and Ulam-Hyers stability (U-Hs) of solutions of a nonlinear neutral stochastic fractional differential system. We prove the existence and uniqueness of solutions to the proposed system by using fixed point theorems and the Banach contrac...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-04-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/6/4/203 |
| _version_ | 1797434735189819392 |
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| author | Manzoor Ahmad Akbar Zada Mehran Ghaderi Reny George Shahram Rezapour |
| author_facet | Manzoor Ahmad Akbar Zada Mehran Ghaderi Reny George Shahram Rezapour |
| author_sort | Manzoor Ahmad |
| collection | DOAJ |
| description | The main purpose of this paper is to investigate the existence and Ulam-Hyers stability (U-Hs) of solutions of a nonlinear neutral stochastic fractional differential system. We prove the existence and uniqueness of solutions to the proposed system by using fixed point theorems and the Banach contraction principle. Also, by using fundamental schemes of fractional calculus, we study the (U-Hs) to the solutions of our suggested system. Besides, we study an example, best describing our main result. |
| first_indexed | 2024-03-09T10:36:43Z |
| format | Article |
| id | doaj.art-d9965e1e90c549bfa208eeac3c617e5c |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T10:36:43Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-d9965e1e90c549bfa208eeac3c617e5c2023-12-01T20:55:23ZengMDPI AGFractal and Fractional2504-31102022-04-016420310.3390/fractalfract6040203On the Existence and Stability of a Neutral Stochastic Fractional Differential SystemManzoor Ahmad0Akbar Zada1Mehran Ghaderi2Reny George3Shahram Rezapour4Department of Mathematics, University of Peshawar, Peshawar 25000, Khyber, PakistanDepartment of Mathematics, University of Peshawar, Peshawar 25000, Khyber, PakistanDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751-71379, IranDepartment of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz 53751-71379, IranThe main purpose of this paper is to investigate the existence and Ulam-Hyers stability (U-Hs) of solutions of a nonlinear neutral stochastic fractional differential system. We prove the existence and uniqueness of solutions to the proposed system by using fixed point theorems and the Banach contraction principle. Also, by using fundamental schemes of fractional calculus, we study the (U-Hs) to the solutions of our suggested system. Besides, we study an example, best describing our main result.https://www.mdpi.com/2504-3110/6/4/203caputo fractional derivativelaplace transformationneutral stochastic fractional differential systemUlam-Hyers stabilityUlam-Hyers-Rassias stability |
| spellingShingle | Manzoor Ahmad Akbar Zada Mehran Ghaderi Reny George Shahram Rezapour On the Existence and Stability of a Neutral Stochastic Fractional Differential System Fractal and Fractional caputo fractional derivative laplace transformation neutral stochastic fractional differential system Ulam-Hyers stability Ulam-Hyers-Rassias stability |
| title | On the Existence and Stability of a Neutral Stochastic Fractional Differential System |
| title_full | On the Existence and Stability of a Neutral Stochastic Fractional Differential System |
| title_fullStr | On the Existence and Stability of a Neutral Stochastic Fractional Differential System |
| title_full_unstemmed | On the Existence and Stability of a Neutral Stochastic Fractional Differential System |
| title_short | On the Existence and Stability of a Neutral Stochastic Fractional Differential System |
| title_sort | on the existence and stability of a neutral stochastic fractional differential system |
| topic | caputo fractional derivative laplace transformation neutral stochastic fractional differential system Ulam-Hyers stability Ulam-Hyers-Rassias stability |
| url | https://www.mdpi.com/2504-3110/6/4/203 |
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