In this paper, a novel fractional-order 2I2SR rumor spreading model is investigated. Firstly, the boundedness and uniqueness of solutions are proved. Then next-generation matrix method used to calculate threshold. Furthermore, stability rumor-free/spreading equilibrium discussed based on Routh–Hurwitz criterion, Lyapunov function method, invariance principle. Next, necessary conditions for frac...

Abstract: In this paper, in order to achieve tracking performance of uncertain fractional order chaotic systems an adaptive hybrid fuzzy controller is proposed. During the design procedure, a hybrid learning algorithm combining sliding mode control and Lyapunov stability criterion is adopted to tune the free parameters on line by output feedback control law and adaptive law. A weighting factor,...

This paper deals with the design of nonlinear PI control techniques for regulating a class of fractional-order dynamics governed by a commensurate-order model, possibly nonlinear, perturbed by an external disturbance. The suggested control algorithm is the combination between a fractional-order PI controller and a nonlinear robust version of it, namely a secondorder sliding mode control algorit...

This paper presents the problem of designing a sliding mode controller via static output feedback for a class of fractional order time-varying mismatched uncertain systems, in which all states are unavailable and estimated states are not required. On the basis of auxiliary system, a sliding mode control law with output feedback characteristics is researched by studying the structure decompositi...

In this article, we extend fractional operators with nonsingular Mittag-Leffler kernels, a study initiated recently by Atangana and Baleanu, from order [Formula: see text] to higher arbitrary order and we formulate their correspondent integral operators. We prove existence and uniqueness theorems for the Caputo ([Formula: see text]) and Riemann ([Formula: see text]) type initial value problems ...

*Correspondence: [email protected] 2College of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, China 3Institute for Information and System Science, Xi’an Jiaotong University, Xi’an, 710049, China Full list of author information is available at the end of the article Abstract This paper is concerned with the Mittag-Leffler stability of fractional-order fuzzy Cohen-Grossberg ...

We present some models of viscoelastic systems with long-memory behaviour; we then provide both thorough mathematical analysis and numerical simulations of these models by means of so-called diiusive representations. The models under consideration are the basic harmonic oscillator with fractional damping, the generalized Lokshin model of waves, and also the boundary feedback control of the Eule...

In this paper, the fractional-order chaotic system form of a four-dimensional with cross-product nonlinearities is introduced. The stability equilibrium points and then feedback control design to achieve goal have been analyzed. Furthermore, further dynamical behaviors including, phase portraits, bifurcation diagrams, largest Lyapunov exponent are presented. Finally, global Mittag–Leffler attra...

The purpose of this paper is to investigate some qualitative properties solutions nonlinear fractional retarded Volterra integro-differential equations (FrRIDEs) with Caputo derivatives. These include uniform stability, asymptotic Mittag–Leffer stability and boundedness. presented results are proved by defining an appropriate Lyapunov function applying the Lyapunov–Razumikhin method (LRM). Henc...