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We investigate the notion of finite time stability for tempered fractional systems (TFSs) with time delays and variable coefficients. Then, we examine some sufficient conditions that allow concluding the TFSs stability in a finite time…
We improve the preceding results obtained by the first and the second authors in [3]. They concern the stability issue of the inverse problem that consists in determining the potential and the damping coefficient in a wave equation from an…
We prove the exponential stability of the zero solution of a stochastic differential equation with a H\"older noise, under the strong dissipativity assumption. As a result, we also prove that there exists a random pullback attractor for a…
This paper is concerned with system of magnetic effected piezoelectric beams with interior time-varying delay and time-dependent weights, in which the beam is clamped at the two side points subject to a single distributed state feedback…
In this paper, we study the long-time stability behavior of a class of linear stochastic evolution equations in a Hilbert space with multiplicative noise. Explicit sufficient conditions for $p$-th moment and almost sure exponential…
This work deals with the existence of an almost periodic solution for certain kind of differential equations with generalized piecewise constant argument, almost periodic coefficients which are seen as a perturbation of a linear equation of…
We establish the best (minimum) constant for Ulam stability of first-order linear $h$-difference equations with a periodic coefficient. First, we show Ulam stability and find the Ulam stability constant for a first-order linear equation…
We consider abstract evolution equations with on-off time delay feedback. Without the time delay term, the model is described by an exponentially stable semigroup. We show that, under appropriate conditions involving the delay term, the…
We present a condition for delay-independent stability of a class of nonlinear positive systems. This result applies to systems that are not necessarily monotone and extends recent work on cooperative nonlinear systems.
This paper deals with stability of a certain class of fractional order linear and nonlinear systems. The stability is investigated in the time domain and the frequency domain. The general stability conditions and several illustrative…
In this paper, we embark on a captivating exploration of the stabilization of locally transmitted problems within the realm of two interconnected wave systems. To begin, we wield the formidable Arendt-Batty criteria\cite{AW} to affirm the…
Existence and stability of time periodic solutions for nonlinear elastic wave equations with viscoelastic terms are established. The existence of the time periodic solution is proved using the spectral decomposition of the linear principal…
We consider a nonlinear non-autonomous system with time-varying delays $$ \dot{x_i}(t)=-a_i(t)x_{i}(h_i(t))+\sum_{j=1}^mF_{ij}(t,x_j(g_{ij}(t))) $$ which has a large number of applications in the theory of artificial neural networks. Via…
Suppose any solution of a linear impulsive delay differential equation $$ \dot{x} (t) + \sum_{i=1}^m A_i (t) x[h_i (t)] = 0,~t \geq 0, x(s) = 0, s < 0, $$ $$ x(\tau_j +0) = B_j x(\tau_j -0) + \alpha_j, ~j=1,2, ... ,$$ is bounded for any…
This paper presents some new criteria for partial exponential stability of a slow-fast nonlinear system with a fast scalar variable using periodic averaging methods. Unlike classical averaging techniques, we construct an averaged system by…
This paper deals with the boundary stabilization problem of a one-dimensional wave equation with a switching time-delay in the boundary. We show that the problem is well-posed in the sense of semigroups theory of linear operators. Then, we…
The solvability and stability analysis of linear time invariant systems of delay differential-algebraic equations (DDAEs) is analyzed. The behavior approach is applied to DDAEs in order to establish characterizations of their solvability in…
In this paper we investigate four concepts of exponential stability for difference equations in Banach spaces. Characterizations of these concepts are given. They can be considered as variants for the discrete-time case of the classical…
This article is focused on two related topics within the study of partial differential equations (PDEs) that illustrate a beautiful connection between dynamics, topology, and analysis: stability and spatial dynamics. The first is a property…
In this work, we study the stabilization of the wave equation using an internal delayed potential. Interestingly, the stabilization mechanism is entirely induced by the delay, since exponential stabilization cannot be achieved in its…