Ulam-Hyers-Rassias Stability of Stochastic Functional Differential Equations via Fixed Point Methods
Abdellatif Ben Makhlouf, Lassaad Mchiri, Mohamed Rhaima
Abstract
The Ulam-Hyers-Rassias stability for stochastic systems has been studied by many researchers using the Gronwall-type inequalities, but there is no research paper on the Ulam-Hyers-Rassias stability of stochastic functional differential equations via fixed point methods. The main goal of this paper is to investigate the Ulam-Hyers Stability (HUS) and Ulam-Hyers-Rassias Stability (HURS) of stochastic functional differential equations (SFDEs). Under the fixed point methods and the stochastic analysis techniques, the stability results for SFDE are investigated. We analyze two illustrative examples to show the validity of the results.
Topics & Concepts
Fixed pointStability (learning theory)MathematicsStochastic differential equationApplied mathematicsFixed-point iterationDifferential (mechanical device)Differential equationPoint (geometry)Computer scienceMathematical analysisMachine learningGeometryEngineeringAerospace engineeringFunctional Equations Stability ResultsNonlinear Differential Equations AnalysisNumerical methods for differential equations