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Our aim in this paper is to investigate the asymptotic behavior of solutions of the perturbed linear fractional differential system. We show that if the original linear autonomous system is asymptotically stable then under the action of…
Sufficient condition for the stability of a fractional order semi-linear system with multi-time delay is proposed.
In this paper, by using a characterization of functions having fractional derivative, we propose a rigorous fractional Lyapunov function candidate method to analyze stability of fractional-order nonlinear systems. First, we prove an…
Fractional derivatives of Prabhakar type are capturing an increasing interest since their ability to describe anomalous relaxation phenomena (in dielectrics and other fields) showing a simultaneous nonlocal and nonlinear behaviour. In this…
The present article considers stability of the solutions to nonlinear and nonautonomous compartmental systems governed by ordinary differential equations (ODEs). In particular, compartmental systems with a right-hand side that can be…
Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the "fractional order…
In this paper, the stability of fractional differential equations (FDEs) with unknown parameters is studied. FDEs bring many advantages to model the physical systems in the nature or man-made systems in the industry. Because this…
In this paper, we give a criterion on instability of an equilibrium of nonlinear Caputo fractional differential systems. More precisely, we prove that if the spectrum of the linearization has at least one eigenvalue in the sector…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
In this article, the order of some classes of fractional linear differential equations is determined, based on asymptotic behavior of the solution as time tends to infinity. The order of fractional derivative has been proved to be of great…
In this paper, we discuss on the linearized stability of the trivial solution for a class of nonlinear Caputo fractional differential systems of order $\alpha\in(1,2)$. We show that some recent existing results in this direction are wrong.…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients are obtained to ensure the stability and instability of…
This study presents new estimates for fractional derivatives without singular kernels defined by some specific functions. Based on obtained inequalities, we give a useful method to establish the global stability of steady states for…
The purpose of this article is to introduce the original results which devoted with the nonlinear control system problems involves of nonlinear differential equations of fractional orders. Thus, this system is described with a mixed of…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
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,…
One of the most popular methods of controlling dynamical systems is feedback. It can be used without acquiring detailed knowledge of the underlying system. In this work, we study the stability of fractional-order linear difference equations…
Invariant manifolds are important sets arising in the stability theory of dynamical systems. In this article, we take a brief review of invariant sets. We provide some results regarding the existence of invariant lines and parabolas in…
This paper considers the problem of robust stability and stabilization for linear fractional-order system with nonlinear uncertain parameters, with fractional order 0<a<2. A dynamic output feedback controller, with predetermined order, for…