Neutral Functional Differential Equations Research Articles

Continuous dependence of a solution of a neutral functional differential equation on the right-hand side and initial data taking into account perturbations of variable delays

Abstract Theorems on the continuous dependence of a solution of the Cauchy problem with respect to the nonlinear term of the right-hand side and initial data are proved for neutral functional differential equations whose right-hand sides are linear with respect to the prehistory of the phase velocity. Under the initial data we imply a collection of initial moment, variable delays entering in the phase coordinates, initial vector and initial functions. In this paper, an essential novelty is that perturbations of variable delays are taken into account in proving the main theorems.

Stabilization of retarded systems of neutral type by control Lyapunov–Krasovskii functionals

This paper deals with the stabilization and the practical stabilization of nonlinear systems described by neutral functional differential equations in Hale’s form, affine in the control input. Artstein’s methodology and Sontag’s universal formula are investigated for this class of systems, by means of invariantly differentiable control Lyapunov–Krasovskii functionals.

Unstable Manifolds for Partial Neutral Differential Equations and Admissibility of Function Spaces

We prove the existence and attraction property of an unstable manifold for solutions to the partial neutral functional differential equation of the form

Global existence results for second order neutral functional differential equation with state-dependent delay

Our aim in this work is to provide sufficient conditions for the existence of global solutions of second order neutral functional differential equation with state-dependent delay. We use the semigroup theory and Schauder's fixed point theorem.

On exponential stability of linear non-autonomous functional differential equations of neutral type

ABSTRACTGeneral linear non-autonomous functional differential equations of neutral type are considered. A novel approach to exponential stability of neutral functional differential equations is presented. Consequently, explicit criteria are derived for exponential stability of linear non-autonomous functional differential equations of neutral type. A brief discussion to the obtained results and illustrative examples are given.

Analytical Exact Solution of Neural Functional-differential Equations

In this paper, we introduce a well-known technique Differential Transform method (DTM) which is very effective to control the convergence region of the approximate solution. The Differential Transform Method is applied to neutral functional-differential equation with proportional delays. The DTM produces an approximate solution with few hand computations without rounding off the error. Obtained solution of Neutral functional-differential equation with proportional delays reveals that DTM is one of the efficient and accurate methods.

Existence of a mild solution for an impulsive nonlocal non-autonomous neutral functional differential equation

This paper considers an impulsive neutral differential equation with nonlocal initial conditions in an arbitrary Banach space E. The existence of the mild solution is obtained by using Krasnoselskii’s fixed point theorem and approximation techniques without imposing the strong restriction on nonlocal function and impulsive functions. An example is also provided at the end of the paper to illustrate the abstract theory.

Oscillation of certain higher-order neutral partial functional differential equations.

In this paper, we study the oscillation of certain higher-order neutral partial functional differential equations with the Robin boundary conditions. Some oscillation criteria are established. Two examples are given to illustrate the main results in the end of this paper.

Exponential stability for stochastic neutral functional differential equations driven by Rosenblatt process with delay and Poisson jumps

Abstract In this note we consider a class of neutral stochastic functional differential equations with finite delays driven simultaneously by a Rosenblatt process and Poisson process in a Hilbert space. We prove an existence and uniqueness result and we establish some conditions ensuring the exponential decay to zero in mean square for the mild solution by means of the Banach fixed point principle. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result.

An averaging principle for neutral stochastic functional differential equations driven by Poisson random measure

In this paper, we study the averaging principle for neutral stochastic functional differential equations (SFDEs) with Poisson random measure. By stochastic inequality, Burkholder-Davis-Gundy’s inequality and Kunita’s inequality, we prove that the solution of the averaged neutral SFDEs with Poisson random measure converges to that of the standard one in $L^{p}$ sense and also in probability. Some illustrative examples are presented to demonstrate this theory.

Global exponential convergence for a class of neutral functional differential equations with proportional delays

This paper is concerned with a class of non‐autonomous neutral functional differential equations with multi‐proportional delays. It is shown that all solutions of the addressed system are globally exponentially convergent by employing the differential inequality technique and a novel argument. The obtained results improve and supplement existing ones. We also use numerical simulations to demonstrate our theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.

Time-dependent neutral stochastic functional differential equations driven by a fractional Brownian motion

Time-dependent neutral stochastic functional differential equations driven by a fractional Brownian motion

Comparison theorems for neutral stochastic functional differential equations

The comparison theorems under Wu and Freedman's order are proved for neutral stochastic functional differential equations with finite or infinite delay whose drift terms satisfy the quasimonotone condition and diffusion term is the same.

Existence of Mild Solutions for Fractional Neutral Functional Differential Equations

Existence of Mild Solutions for Fractional Neutral Functional Differential Equations

Research on the Numerical Analysis of Nonlinear Neutral Functional Differential Equations

Research on the Numerical Analysis of Nonlinear Neutral Functional Differential Equations

Periodic Solutions in UMD Spaces for Some Neutral Partial Functional Differential Equations

The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the R-boundedness of linear operators Lp-multipliers and UMD-spaces.

Measure of Noncompactness and Neutral Functional Differential Equations with State-Dependent Delay

Measure of Noncompactness and Neutral Functional Differential Equations with State-Dependent Delay

On the existence and uniqueness of periodic solution for a third-order neutral functional differential equation

On the existence and uniqueness of periodic solution for a third-order neutral functional differential equation

EXISTENCE OF <i>µ</i>-PSEUDO ALMOST AUTOMORPHIC SOLUTIONS TO ABSTRACT PARTIAL NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

In this article, we introduce and investigate the concept of <i>µ</i>-Stepanov-like pseudo almost automorphic functions of class <i>h</i> and class infinity via measure theory. We present new results on completeness and composition theorems for the space of such functions. To illustrate our main results, we provide some applications to an abstract partial neutral functional differential equation with infinite delay.

Global attractiveness and quasi-invariant sets of impulsive neutral stochastic functional differential equations driven by fBm

In this paper, we are concerned with a class of impulsive neutral stochastic functional differential equations driven by fractional Brownian motion in the Hilbert space. We obtain the global attracting and quasi-invariant sets of this kind of equations driven by fractional Brownian motion with Hurst parameter H∈(1/2,1). Especially, the sufficient conditions ensuring the exponential p-stability of the mild solution of the considered equations are obtained. In the end, one example is given to illustrate the feasibility and effectiveness of results obtained.