Open AccessA remark on the stability and boundedness criteria in retarded Volterra integro-differential equations
Author(s) -
Cemil Tunç,
Sizar Abid Mohammed
Publication year - 2017
Publication title -
journal of the egyptian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2090-9128
pISSN - 1110-256X
DOI - 10.1016/j.joems.2017.05.001
Subject(s) - mathematics , volterra equations , stability (learning theory) , volterra integral equation , differential equation , mathematical analysis , integral equation , nonlinear system , computer science , physics , quantum mechanics , machine learning
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, 45J0