A remark on the stability and boundedness criteria in retarded Volterra integro-differential equations | Zendy

Cemil Tunç | Zendy; Sizar Abid Mohammed | Zendy

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A 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 , stability (learning theory) , differential equation , order (exchange) , volterra integral equation , exponential stability , volterra equations , differential (mechanical device) , mathematical analysis , nonlinear system , integral equation , computer science , quantum mechanics , machine learning , finance , aerospace engineering , engineering , economics , physics

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

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