On behaviours for the solution to a certain third-order stochastic integro-differential equation with time delay

Abstract

In the present paper, Lyapunov functional (LF) is employed to discuss the continuability and boundedness of solutions for a third-order non-autonomous stochastic integro-differential equation (SIDE) with time delay. The third-order differential equation is ablated to a system of first-order differential equations together with its equivalent quadratic function to derive a suitable downright LF and then we study the behaviour of the solutions. A numerical example is considered to support our results. Moreover, we use the Euler-Maruyama method to prove an approximate numerical solution for the considered system. The obtained result complements some recent ones in the literature