The literature of neural network models has been intensively established in the last two decades. As one of the most interested topics of studying the dynamics of a neural networks system, parametrical-induced, dynamical stability draws a vast majority of attention in the recent years of researches. For examples, in their recent study, Akhmet & Yilmaz 2009 considered the Hopfield type neural ne...

Using a technique of monotonization, this paper investigates a generalized GronwallBellman type delay integral inequality with two independent variables on time scales. The result not only unifies some continuous inequalities and their discrete analogues but also extends some known integral inequalities on time scales. An application to the estimation of solutions of delay dynamic integral equa...

In this paper, an iterative learning control topic for a kind of singular distributed parameter system with forgetting with time-delay which initial value can vary in a little space has been discussed. And a high level algorithm is extended and proven, using Green formula and Gronwall inequality, that it is suitable for the given system. Convergence of the proposed approach is analyzed and the ...

The purpose of this article is to show how the solution of the linear quasistatic (compressible) viscoelasticity problem, written in Volterra form with fading memory, may be sharply bounded in terms of the data if certain physically reasonable assumptions are satissed. The bounds are derived by making precise assumptions on the memory term which then make it possible to avoid the Gronwall inequ...

The main intention of the present research study is focused on analysis a Caputo fractional integro-differential boundary problem (CFBVP) in which right-hand side supposed differential equation represented as sum two nonlinear terms. Under integro-derivative conditions, we extract an equivalent integral and then define new operators based it. With help three distinct fixed-point theorems attrib...

This paper studies the iterative learning control (ILC) for a class of second-order nonlinear hyperbolic impulsive partial differential systems. Firstly, to follow discontinuous desired output, P-type law is adopted, and sufficient conditions convergence tracking error established under identified initial state value. The rigorous analysis also given using Gronwall inequality. Secondly, output ...

In this paper we present an error analysis for a second order accurate numerical scheme the 2-D and 3-D Cahn–Hilliard (CH) equation, with improved convergence constant. The unique solvability, unconditional energy stability, uniform-in-time H2 stability of have already been established. However, standard estimate gives constant in exp(CT??m0), m0 positive integer interface width parameter ? bei...

The problem of adaptive output tracking is researched for a class of nonlinear network control systems with parameter uncertainties and time-delay. In this paper, a new program is proposed to design a state-feedback controller for this system. For time-delay and parameter uncertainties problems in network control systems, applying the backstepping recursive method, and using Young inequality to...

The main objective of the present paper is to establish some new Gronwall type inequalities involving iterated integrals.