In this paper, we use the fixed point theorem to obtain stability results of the zero solution of a nonlinear neutral system of differential equations with functional delay. Application to the second-order model is given with an example. AMS (MOS) Subject Classification. 34K20, 34K40, 34A34, 35A08.

This paper is concerned with a class of partial nonlocal neutral functional differential and integrodifferential equations with bounded delay in Banach spaces, which are more general than those models been studied. Some existence results of mild solutions to such problems are obtained under the conditions in respect of the Hausdorff’s measure of noncompactness.

In this article, we have dealt with the controllability for impulsive (Imp.) neutral fractional functional integro-differential equations with state dependent delay (S-D Delay) subject to non-local conditions. We have obtained the appropriate conditions for Controllability result by using the classical fixed point technique and analytic operator theory under the more general conditions. At last...

In this paper we study the existence of classical solutions for a class of abstract neutral integro-differential equation with unbounded delay. A concrete application to partial neutral integro-differential equations is considered.

Sufficient conditions of interval absolute stability of nonlinear control systems described in terms of systems of the ordinary differential equations with delay argument and also neutral type are obtained. The Lyapunov-Krasovskii functional method in the form of the sum of a quadratic component and integrals from nonlinearity is used at construction of statements.

In this paper, which is a direct continuation and generalization of the recent works by authors [17, 35], we show validity generic multiplicity-induced-dominancy property for general class linear functional differential equations with single delay, including retarded as well neutral cases. The result based on an appropriate integral representation corresponding characteristic quasipolynomial fu...

In this paper we study the dissipativity of a special class of nonlinear neutral delay integro-differential equations. The dissipativity of three kinds of important numerical methods, the linear θ-methods, one-leg θmethods, and the one-leg methods is obtained when they are applied to these problems. Numerical experiments are presented to check our findings. Key–Words: Linear θ-methods, One-leg ...