Related papers: A linearized stability theorem for nonlinear delay…
We examine the phenomenon of nonlinear stabilization, exhibiting a variety of related examples and counterexamples. For G\^ateaux differentiable maps, we discuss a mechanism of nonlinear stabilization, in finite and infinite dimensions,…
In this article, we give some results for fractional-order delay differential equations. In the first result, we prove the existence and uniqueness of solution by using Bielecki norm effectively. In the second result, we consider a constant…
We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
This paper deals with the stability analysis of a nonlinear time-delayed dispersive equation of order four. First, we prove the well-posedness of the system and give some regularity results. Then, we show that the zero solution of the…
In this paper, we prove nonlinear orbital stability for steady vortex patches that maximize the kinetic energy among isovortical rearrangements in a planar bounded domain. As a result, nonlinear stability for an isolated vortex patch is…
This paper proposes an unconditionally stable numerical method for solving a nonlinear Sobolev model with distributed delay. The proposed computational approach approximates the time derivative by interpolation technique whereas the spatial…
Here we are concerned about uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its two ends. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess…
In this paper, stability and synchronization of a Caputo fractional BAM neural network system of high-order type and neutral delays are examined. A mixture of properties of fractional calculus, Laplace transform, and analytical techniques…
This paper is devoted to studying three-dimensional non-commensurate fractional order differential equation systems with Caputo derivatives. Necessary and sufficient conditions are for the asymptotic stability of such systems are obtained.
We investigate discret conditions for stability and asymptotic stability by Lyapunov and the point of equilibrium of autonomous system of differential equations.
Sufficient condition for the stability of a fractional order semi-linear system with multi-time delay is proposed.
This paper addresses the stabilization issue for fractional order switching systems. Common Lyapunov method is generalized for fractional order systems and frequency domain stability equivalent to this method is proposed to prove the…
Caputo fractional (with power-law kernels) and fractional (delta) difference maps belong to a more widely defined class of generalized fractional maps, which are discrete convolutions with some power-law-like functions. The conditions of…
This paper establishes new sufficient conditions for Mittag-Leffler stability of Caputo fractional-order nonlinear systems with state-dependent delays. The central analytical tool is a class of Lyapunov-Krasovskii functionals that…
This paper is devoted to the study of Lyapunov type inequalities for periodic conservative systems. The main results are derived from a previous analysis which relates the best Lyapunov constants to some especial (constrained or…
Necessary and sufficient stability and instability conditions are obtained for multi-term homogeneous linear fractional differential equations with three Caputo derivatives and constant coefficients. In both cases,…
In this paper we consider a nonlinear Petrovsky equation in a bounded domain with a delay term and a strong dissipation \begin{align*} u_{tt} + \Delta^{2} u -\mu_1g_1( \Delta( u_t(x,t))) -\mu_2g_2( \Delta (u_t(x,t-\tau))) =0. \end{align*}…
We give sufficient conditions such that the exponential stability of the linearization of a non-linear system implies that the non-linear system is (locally) exponentially stable. One of these conditions is that the non-linear system is…
We study semilinear rough stochastic partial differential equations as introduced in [Gerasimovi{\v{c}}s, Hairer; EJP 2019]. We provide $\mathcal{L}^p(\Omega)$-integrable a priori bounds for the solution and its linearization in case the…