Some Existence, Uniqueness, and Stability Results for a Class of <i>ϑ</i>-Fractional Stochastic Integral Equations
This paper focuses on the existence and uniqueness of solutions for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϑ</mi></semantics></math></inline-formula>-fractional stochastic in...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-12-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/9/1/7 |
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| author | Fahad Alsharari Raouf Fakhfakh Omar Kahouli Abdellatif Ben Makhlouf |
| author_facet | Fahad Alsharari Raouf Fakhfakh Omar Kahouli Abdellatif Ben Makhlouf |
| author_sort | Fahad Alsharari |
| collection | DOAJ |
| description | This paper focuses on the existence and uniqueness of solutions for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϑ</mi></semantics></math></inline-formula>-fractional stochastic integral equations (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϑ</mi></semantics></math></inline-formula>-FSIEs) using the Banach fixed point theorem (BFPT). We explore the Ulam–Hyers stability (UHS) of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϑ</mi></semantics></math></inline-formula>-FSIEs through traditional methods of stochastic calculus and the BFPT. Moreover, the continuous dependence of solutions on initial conditions is proven. Additionally, we provide three examples to demonstrate our findings. |
| format | Article |
| id | doaj-art-2d4b7f3fe60440eda84a1955eba3c02f |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-2d4b7f3fe60440eda84a1955eba3c02f2025-01-24T13:33:21ZengMDPI AGFractal and Fractional2504-31102024-12-0191710.3390/fractalfract9010007Some Existence, Uniqueness, and Stability Results for a Class of <i>ϑ</i>-Fractional Stochastic Integral EquationsFahad Alsharari0Raouf Fakhfakh1Omar Kahouli2Abdellatif Ben Makhlouf3Department of Mathematics, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi ArabiaDepartment of Mathematics, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi ArabiaDepartment of Electronics Engineering, Applied College, University of Ha’il, Ha’il 2440, Saudi ArabiaDepartment of Mathematics, Faculty of Sciences, Sfax University, BP 1171, Sfax 3000, TunisiaThis paper focuses on the existence and uniqueness of solutions for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϑ</mi></semantics></math></inline-formula>-fractional stochastic integral equations (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϑ</mi></semantics></math></inline-formula>-FSIEs) using the Banach fixed point theorem (BFPT). We explore the Ulam–Hyers stability (UHS) of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϑ</mi></semantics></math></inline-formula>-FSIEs through traditional methods of stochastic calculus and the BFPT. Moreover, the continuous dependence of solutions on initial conditions is proven. Additionally, we provide three examples to demonstrate our findings.https://www.mdpi.com/2504-3110/9/1/7fractional integral with respect to another functionstochastic calculusUlam–Hyers stability |
| spellingShingle | Fahad Alsharari Raouf Fakhfakh Omar Kahouli Abdellatif Ben Makhlouf Some Existence, Uniqueness, and Stability Results for a Class of <i>ϑ</i>-Fractional Stochastic Integral Equations Fractal and Fractional fractional integral with respect to another function stochastic calculus Ulam–Hyers stability |
| title | Some Existence, Uniqueness, and Stability Results for a Class of <i>ϑ</i>-Fractional Stochastic Integral Equations |
| title_full | Some Existence, Uniqueness, and Stability Results for a Class of <i>ϑ</i>-Fractional Stochastic Integral Equations |
| title_fullStr | Some Existence, Uniqueness, and Stability Results for a Class of <i>ϑ</i>-Fractional Stochastic Integral Equations |
| title_full_unstemmed | Some Existence, Uniqueness, and Stability Results for a Class of <i>ϑ</i>-Fractional Stochastic Integral Equations |
| title_short | Some Existence, Uniqueness, and Stability Results for a Class of <i>ϑ</i>-Fractional Stochastic Integral Equations |
| title_sort | some existence uniqueness and stability results for a class of i ϑ i fractional stochastic integral equations |
| topic | fractional integral with respect to another function stochastic calculus Ulam–Hyers stability |
| url | https://www.mdpi.com/2504-3110/9/1/7 |
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