Some Existence, Uniqueness, and Stability Results for a Class of <i>ϑ</i>-Fractional Stochastic Integral Equations

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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Bibliographic Details
Main Authors:	Fahad Alsharari, Raouf Fakhfakh, Omar Kahouli, Abdellatif Ben Makhlouf
Format:	Article
Language:	English
Published:	MDPI AG 2024-12-01
Series:	Fractal and Fractional
Subjects:	fractional integral with respect to another function stochastic calculus Ulam–Hyers stability
Online Access:	https://www.mdpi.com/2504-3110/9/1/7
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Summary:	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.
ISSN:	2504-3110