| Summary: | In this article, the authors obtain some clear assumptions for the asymptotic stability (AS) and boundedness (B) of solutions of non-linear retarded Volterra integro-differential equations (VIDEs) of first order by constructing a new Lyapunov functional (LF). The results obtained are new and differ from those found in the literature, and they also contain and improve a result found in the literature under more less restrictive conditions. We establish an example and give a discussion to indicate the applicability of the weaker conditions obtained. We also employ MATLAB-Simulink to display the behaviors of the orbits of the (VIDEs) considered. Keywords: Nonlinear, Volterra integro-differential equations, First order, Asymptotic stability, Boundedness, Lyapunov functional, MSC: 34D05, 34K20, 45J05
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