Asymptotic stability and boundedness criteria for nonlinear retarded Volterra integro-differential equations

In this article, we construct new specific conditions for the asymptotic stability (AS) and boundedness (B) of solutions to nonlinear Volterra integro-differential equations (VIDEs) of first order with a constant retardation. Our analysis is based on the successful construction of suitable Lyapunov–Krasovskii functionals (LKFs). The results of this paper are new, and they improve and complete that can be found in the literature. Keywords: Volterra integro-differential equation, First order, Retardation, Asymptotic stability, Boundedness, Lyapunov–Krasovskii functional