In this paper, the finite-time stability for nonlinear neutral multi-term fractional order systems with time-varying input and state delays is investigated. By use of generalized Gronwall inequality extended form inequality, new sufficient conditions such are obtained. Finally, numerical examples given to illustrate effectiveness applicability proposed theoretical results.

In this note, two theorems are presented concerning the well known second order linear differential system Ẍ +a(t)X =P(t). While the results are not new, the proofs presented simplify previous works since the Gronwall inequality is avoided which is the usual case. The technique of proof involves the integral test and examples are included to illustrate the results.

The stability of n-dimensional linear fractional differential systems with commensurate order 1 < α < 2 and the corresponding perturbed systems is investigated. By using the Laplace transform, the asymptotic expansion of the Mittag-Leffler function, and the Gronwall inequality, some conditions on stability and asymptotic stability are given.

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, stochastic functional differential equations with impulses are considered. By employing Gronwall-Bellman inequality, the stochastic analytic technique and the properties of operator semigroup, the sufficient con...

We study the long time asymptotic behavior of solutions to a class of fourth-order nonlinear evolution equations with dispersive and dissipative terms. By using the integral estimation method combined with the Gronwall inequality, we point out that the global strong solutions of the problems decay to zero exponentially with the passage of time to infinity. The proof is rigorous and only based o...

In this paper, we introduce an innovative and systematic technique to study delay differential equations via polynomials. First, we review an intrinsic relation between delay differential equations and polynomials. From this relation, we obtain long time behaviors of the solutions to delay differential equations via asymptotic analysis of the corresponding polynomials. Moreover, we derive asymp...

In this paper, based on the estimation of the Cauchy matrix of linear impulsive differential equations, by using Banach fixed point theorem and Gronwall-Bellman’s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solution for Cohen-Grossberg shunting inhibitory cellular neural networks (SICNNs) with continuously distributed delays...

The problems of mean-square exponential stability and robust H∞ control of switched stochastic systems with time-varying delay are investigated in this paper. Based on the average dwell time method and Gronwall-Bellman inequality, a new mean-square exponential stability criterion of such system is derived in terms of linear matrix inequalities LMIs . Then, H∞ performance is studied and robust H...

This work addresses the asymptotic stability for a class of impulsive cellular neural networks with time-varying delays and reaction-diffusion. By using the impulsive integral inequality of Gronwall-Bellman type and Hardy-Sobolev inequality as well as piecewise continuous Lyapunov functions, we summarize some new and concise sufficient conditions ensuring the global exponential asymptotic stabi...