On asymptotically stability, uniformly stability and boundedness of solutions of nonlinear Volterra integro-differential equations

C. Tunç; S. A.  Mohammed

doi:10.37863/umzh.v72i12.6037

C. Tunç College Basic Education, Univ. Duhok, Iraq
S. A. Mohammed College Basic Education, Univ. Duhok, Iraq

DOI: https://doi.org/10.37863/umzh.v72i12.6037

Keywords: Non-linear, first order

Abstract

UDC 517.9

In this paper, two new Lyapunov functionals are defined.
We apply these functionals to get sufficient conditions guaranteeing the asymptotic stability, uniform stability, and boundedness of solutions of certain nonlinear Volterra integro-differential equations of the first order.
The results obtained are improvements and extensions of known results that can be found in literature.
We also suggest examples to show the applicability of our results and for the sake of illustrations.
Using MATLAB-Simulink, in particular cases we clearly show the behavior of orbits of Volterra integro-differential equations under consideration.

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