Ulam–Hyers stability for second-order non-instantaneous impulsive fractional neutral stochastic differential equations

Abstract

In this paper, sufficient conditions are established for the Ulam–Hyers stability of second-order non-instantaneous impulsive fractional neutral stochastic differential equations (NIIFNSDEs) with supremum norm in the pth means square sense. The existence of solution of NIIFNSDEs is derived by using the cosine family of linear operator, Itô’s formula, and Mönch fixed point theorem in infinite-dimensional space. Finally, an example is demonstrated to illustrate the obtained theoretical results.