Related papers: Fractional Stability
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
The issues of robust stability for two types of uncertain fractional-order systems of order $\alpha \in (0,1)$ are dealt with in this paper. For the polytope-type uncertainty case, a less conservative sufficient condition of robust…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
The paper is devoted to the development of control procedures with a guide for conflict-controlled dynamical systems described by ordinary fractional differential equations with the Caputo derivative of an order $\alpha \in (0, 1).$ For the…
We consider a fractional generalization of Hamiltonian and gradient systems. We use differential forms and exterior derivatives of fractional orders. We derive fractional generalization of Helmholtz conditions for phase space. Examples of…
In this paper quotients of control systems which are generalizations of system reductions are used to study the stabilizability property of non-linear systems. Given a control system and its quotient we study under what conditions…
The fractional stable motion is a prototypical stochastic process exhibiting both heavy tails and long-range dependence, parameterized via a stability index $\alpha$ and a Hurst exponent $H$. We consider a nonstationary extension where the…
Lyapunov's theorem provides a fundamental characterization of the stability of dynamical systems. This paper presents a categorical framework for Lyapunov theory, generalizing stability analysis with Lyapunov functions categorically. Core…
The normalization condition, average values and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
We study a fractional reaction-diffusion system with two types of variables: activator and inhibitor. The interactions between components are modeled by cubical nonlinearity. Linearization of the system around the homogeneous state provides…
Stability and stabilization analysis of fractional-order linear time-invariant (FO-LTI) systems with different derivative orders is studied in this paper. First, by using an appropriate linear matrix function, a single-order equivalent…
We study the process of dispersion of low-regularity solutions to the Schr\"odinger equation using fractional weights (observables). We give another proof of the uncertainty principle for fractional weights and use it to get a lower bound…
In this work characterizations of notions of output stability for uncertain time-varying systems described by retarded functional differential equations are provided. Particularly, characterizations by means of Lyapunov and Razumikhin…
Using kicked differential equations of motion with derivatives of noninteger orders, we obtain generalizations of the dissipative standard map. The main property of these generalized maps, which are called fractional maps, is long-term…
In the present paper, we address a class of the fractional derivatives of constant and variable orders for the first time. Fractional-order relaxation equations of constants and variable orders in the sense of Caputo type are modeled from…
The main purpose of this paper is to present a general method for the controllability of the stability of a system of fractional-order differential equations around its equilibrium states. This method is applied to analyze and control the…
Necessary and sufficient conditions are explored for the asymptotic stability and instability of linear two-dimensional autonomous systems of fractional-order differential equations with Caputo derivatives. Fractional-order-dependent and…
Intrinsic instability of trajectories characterizes chaotic dynamical systems. We report here that trajectories can exhibit a surprisingly high degree of stability, over a very long time, in a chaotic dynamical system. We provide a detailed…