Related papers: An instability theorem for nonlinear fractional di…
In this paper we propose a method to define the range of stability of fixed points for a variety of discrete fractional systems of the order $0 < \alpha <2$. The method is tested on various forms of fractional generalizations of the…
The principle of linearized stability and instability is established for a classical model describing the spatial movement of an age-structured population with nonlinear vital rates. It is shown that the real parts of the eigenvalues of the…
This paper is devoted to the investigation of the nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic systems involving delayed dynamics with point delays. The obtained…
A noisy damping parameter in the equation of motion of a nonlinear oscillator renders the fixed point of the system unstable when the amplitude of the noise is sufficiently large. However, the stability diagram of the system can not be…
For two-dimensional autonomous linear incommensurate fractional-order dynamical systems with Caputo derivatives of different orders, necessary and sufficient conditions are obtained for the asymptotic stability and instability of the null…
In this paper, we investigate the scaling invariance of survival probability in the Caputo fractional standard map of the order $1<\alpha<2$ considered on a cylinder. We consider relatively large values of the nonlinearity parameter $K$ for…
Based on the generalized Routh-Hurwitz criterion, we propose a sufficient and necessary criterion for testing the stability of fractional-order linear systems with order {\alpha}{\in}[1,2), called the fractional-order Routh-Hurwitz…
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…
This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…
This paper derives two stabilizability theorems for a basic class of discrete-time nonlinear systems with multiple unknown parameters. First, we claim that a discrete-time multi-parameter system is stabilizable if its nonlinear growth rate…
We study the dynamics of a quantum system having Hilbert space of finite dimension $d_{\mathrm{H}}$. Instabilities are possible provided that the master equation governing the system's dynamics contain nonlinear terms. Here we consider the…
A fractional generalization of variations is used to define a stability of non-integer order. Fractional variational derivatives are suggested to describe the properties of dynamical systems at fractional perturbations. We formulate…
Using Caputo fractional derivative of order $\alpha,$ $\alpha\in (0,1),$ we consider some chaotic systems of fractional differential equation. We will prove that they can be synchronized and anti-synchronized using suitable nonlinear…
The main purpose of this paper is to study the fractional-order system with Caputo derivative associated to single Stokes pulse. The dynamic behavior for this fractional model (called the fractional Stokes system) is investigated,…
We examine the stability of a 1D electrical transmission line in the simultaneous presence of PT-symmetry and fractionality. The array contains a binary gain/loss distribution $\gamma_{n}$ and a fractional Laplacian characterized by a…
This paper is devoted to studying the asymptotic behaviour of solutions to generalized non-commensurate fractional systems. To this end, we first consider fractional systems with rational orders and introduce a criterion that is necessary…
A criterion on the asymptotic stability of fractional-order systems with incomensurate orders is proposed in this paper. Existing methods always assume order parameters be rational numbers or the ratios of any two orders be rational…
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…
In this paper the non-linear wave equation with a spatial inhomogeneity is considered. The inhomogeneity splits the unbounded spatial domain into three or more intervals, on each of which the non-linear wave equation is homogeneous. In such…
The main purpose of this paper is to study the fractional-order model with Caputo derivative associated to Lagrange system. For this fractional-order system we investigate the existence and uniqueness of solutions of initial value problem,…