Lur’e Postnikov Lyapunov functional technique to global Mittag-Leffler stability of fractional-order neural networks with piecewise constant argument

International audienc

Mittag-Leffler state estimator design and synchronization analysis for fractional order BAM neural networks with time delays

This paper deals with the extended design of Mittag-Leffler state estimator and adaptive synchronization for fractional order BAM neural networks (FBNNs) with time delays. By the aid of Lyapunov direct approach and Razumikhin-type method a suitable fractional order Lyapunov functional is constructed and a new set of novel sufficient condition are derived to estimate the neuron states via available output measurements such that the ensuring estimator error system is globally Mittag-Leffler stable. Then, the adaptive feedback control rule is designed, under which the considered FBNNs can achieve Mittag-Leffler adaptive synchronization by means of some fractional order inequality techniques. Moreover, the adaptive feedback control may be utilized even when there is no ideal information from the system parameters. Finally, two numerical simulations are given to reveal the effectiveness of the theoretical consequences.N/

Practical stability for fractional impulsive control systems with noninstantaneous impulses on networks

This paper investigates practical stability for a class of fractional-order impulsive control coupled systems with noninstantaneous impulses on networks. Using graph theory and Lyapunov method, new criteria for practical stability, uniform practical stability as well as practical asymptotic stability are established. In this paper, we extend graph theory to fractional-order system via piecewise Lyapunov-like functions in each vertex system to construct global Lyapunov-like functions. Our results are generalization of some known results of practical stability in the literature and provide a new method of impulsive control law for impulsive control systems with noninstantaneous impulses. Examples are given to illustrate the effectiveness of our result

Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations

This article, we explore the asymptotic stability and asymptotic synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous neuron activation functions (FCGNNDDs). First, under the framework of Filippov theory and differ- ential inclusion theoretical analysis, the global existence of Filippov solution for FCGNNDDs is studied by means of the given growth condition. Second, by virtue of suitable Lyapunov functional, Young inequality and comparison theorem for fractional order delayed linear system, some global asymptotic stability conditions for such system is derived by limiting discontinuous neuron activations. Third, the global asymptotic synchronization condition for FCGNNDDs is obtained based on the pinning control. At last, two numerical simula- tions are given to verify the theoretical findings.N/

Finite-time projective synchronization of fractional-order delayed quaternion-valued fuzzy memristive neural networks

In this paper, the finite-time projective synchronization (FTPS) problem of fractionalorder quaternion-valued fuzzy memristor neural networks (FOQVFMNNs) is studied. Through establishing a feedback controller with signed functions and an adaptive controller, sufficient conditions for FTPS for FOQVFMNNs are obtained. Furthermore, the synchronization establishment time is calculated. Finally, the practicability of the conclusions is verified by numerical simulations

Fractional Calculus - Theory and Applications

In recent years, fractional calculus has led to tremendous progress in various areas of science and mathematics. New definitions of fractional derivatives and integrals have been uncovered, extending their classical definitions in various ways. Moreover, rigorous analysis of the functional properties of these new definitions has been an active area of research in mathematical analysis. Systems considering differential equations with fractional-order operators have been investigated thoroughly from analytical and numerical points of view, and potential applications have been proposed for use in sciences and in technology. The purpose of this Special Issue is to serve as a specialized forum for the dissemination of recent progress in the theory of fractional calculus and its potential applications

The 2nd International Conference on Mathematical Modelling in Applied Sciences, ICMMAS’19, Belgorod, Russia, August 20-24, 2019 : book of abstracts

The proposed Scientific Program of the conference is including plenary lectures, contributed oral talks, poster sessions and listeners. Five suggested special sessions / mini-symposium are also considered by the scientific committe

Dynamics of a Fractional-Order Delayed Model of COVID-19 with Vaccination Efficacy

In this study, we provide a fractional-order mathematical model that considers the effect of vaccination on COVID-19 spread dynamics. The model accounts for the latent period of intervention strategies by incorporating a time delay τ. A basic reproduction number, R0, is determined for the model, and prerequisites for endemic equilibrium are discussed. The model’s endemic equilibrium point also exhibits local asymptotic stability (under certain conditions), and a Hopf bifurcation condition is established. Different scenarios of vaccination efficacy are simulated. As a result of the vaccination efforts, the number of deaths and those affected have decreased. COVID-19 may not be effectively controlled by vaccination alone. To control infections, several non-pharmacological interventions are necessary. Based on numerical simulations and fitting to real observations, the theoretical results are proven to be effective