Title of article :
Existence and Stability of Ulam–Hyers for Neutral Stochastic Functional Differential Equations
Author/Authors :
Selvam ، Arunachalam Department of Mathematics - Faculty of Engineering and Technology - SRM Institute of Science Technology , Sabarinathan ، Sriramulu Department of Mathematics - Faculty of Engineering and Technology - SRM Institute of Science Technology , Pinelas ، Sandra Departamento de Ciências Exatas e Engenharia - Academia Militar , Suvitha ، Vaidhiyanathan Department of Mathematics - Faculty of Engineering and Technology - SRM Institute of Science Technology
Abstract :
The primary aim of this paper is to focus on the stability analysis of an advanced neural stochastic functional differential equation with finite delay driven by a fractional Brownian motion in a Hilbert space. We examine the existence and uniqueness of mild solution of d [xa(s) + g(s, xa(s − ω(s)))] = [Ixa(s) + f(s, xa (s − (s)))] ds+ ς (s)d ω¯H(s), 0 ≤ s ≤ T, xa(s) = ζ (s), −ρ ≤ s ≤ 0. The main goal of this paper is to investigate the Ulam–Hyers stability of the considered equation. We have also provided numerical examples to illustrate the obtained results. This article also discusses the Euler–Maruyama numerical method through two examples.
Keywords :
Fractional Brownian motion , Mild solution , Stochastic neutral functional differential equation , Ulam–Hyers stability
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
