Some results on proportional Caputo neutral fractional stochastic differential equations
Abdellatif Ben Makhlouf, Jihen Sallay
Abstract
This paper explores Proportional Neutral Fractional Stochastic Differential Equations (PNFSDEs), emphasizing their existence, uniqueness, and Hyers-Ulam Stability (HUS). The continuous dependence of solutions on initial data and their regularity in time are also established. By using the Banach Fixed Point Theorem (BFPT), Itô's isometry formula, and some classical inequalities, we obtain the theoretical findings. Finally, we present an example to illustrate the effectiveness of our results.
Topics & Concepts
Stochastic differential equationMathematicsApplied mathematicsDifferential equationMathematical analysisFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisMathematical functions and polynomials