Existence and Uniqueness Results for a Class of Fractional Integro-Stochastic Differential Equations
The objective of this paper is to demonstrate the existence and uniqueness (EU) of solutions to a class of Fractional Integro-Stochastic Differential Equations (FISDEs) by utilizing the fixed-point technique (FPT) and stochastic techniques. Additionally, the paper proves the continuous dependence (C...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-01-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/1/42 |
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| author | Ayed. R. A. Alanzi Shokrya S. Alshqaq Raouf Fakhfakh Abdellatif Ben Makhlouf |
| author_facet | Ayed. R. A. Alanzi Shokrya S. Alshqaq Raouf Fakhfakh Abdellatif Ben Makhlouf |
| author_sort | Ayed. R. A. Alanzi |
| collection | DOAJ |
| description | The objective of this paper is to demonstrate the existence and uniqueness (EU) of solutions to a class of Fractional Integro-Stochastic Differential Equations (FISDEs) by utilizing the fixed-point technique (FPT) and stochastic techniques. Additionally, the paper proves the continuous dependence (CD) of solutions on the initial data. We examine the Hyers–Ulam stability (HUS) of FISDEs by applying Gronwall inequalities. Two theoretical examples are presented to demonstrate our findings. |
| format | Article |
| id | doaj-art-9a564542bc34413c81d5882dc22340a2 |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-9a564542bc34413c81d5882dc22340a22025-01-24T13:33:28ZengMDPI AGFractal and Fractional2504-31102025-01-01914210.3390/fractalfract9010042Existence and Uniqueness Results for a Class of Fractional Integro-Stochastic Differential EquationsAyed. R. A. Alanzi0Shokrya S. Alshqaq1Raouf Fakhfakh2Abdellatif Ben Makhlouf3Department of Mathematics, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi ArabiaDepartment of Mathematics, College of Science, Jazan University, P.O. Box 114, Jazan 45142, Saudi ArabiaDepartment of Mathematics, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi ArabiaDepartment of Mathematics, Faculty of Sciences, Sfax University, Sfax BP 1171, TunisiaThe objective of this paper is to demonstrate the existence and uniqueness (EU) of solutions to a class of Fractional Integro-Stochastic Differential Equations (FISDEs) by utilizing the fixed-point technique (FPT) and stochastic techniques. Additionally, the paper proves the continuous dependence (CD) of solutions on the initial data. We examine the Hyers–Ulam stability (HUS) of FISDEs by applying Gronwall inequalities. Two theoretical examples are presented to demonstrate our findings.https://www.mdpi.com/2504-3110/9/1/42Caputo derivativeHadamard fractional integralstability |
| spellingShingle | Ayed. R. A. Alanzi Shokrya S. Alshqaq Raouf Fakhfakh Abdellatif Ben Makhlouf Existence and Uniqueness Results for a Class of Fractional Integro-Stochastic Differential Equations Fractal and Fractional Caputo derivative Hadamard fractional integral stability |
| title | Existence and Uniqueness Results for a Class of Fractional Integro-Stochastic Differential Equations |
| title_full | Existence and Uniqueness Results for a Class of Fractional Integro-Stochastic Differential Equations |
| title_fullStr | Existence and Uniqueness Results for a Class of Fractional Integro-Stochastic Differential Equations |
| title_full_unstemmed | Existence and Uniqueness Results for a Class of Fractional Integro-Stochastic Differential Equations |
| title_short | Existence and Uniqueness Results for a Class of Fractional Integro-Stochastic Differential Equations |
| title_sort | existence and uniqueness results for a class of fractional integro stochastic differential equations |
| topic | Caputo derivative Hadamard fractional integral stability |
| url | https://www.mdpi.com/2504-3110/9/1/42 |
| work_keys_str_mv | AT ayedraalanzi existenceanduniquenessresultsforaclassoffractionalintegrostochasticdifferentialequations AT shokryasalshqaq existenceanduniquenessresultsforaclassoffractionalintegrostochasticdifferentialequations AT raouffakhfakh existenceanduniquenessresultsforaclassoffractionalintegrostochasticdifferentialequations AT abdellatifbenmakhlouf existenceanduniquenessresultsforaclassoffractionalintegrostochasticdifferentialequations |