In this paper, a class of fractional order systems is considered and simple fractional order observers have been proposed to estimate the system’s state variables. By introducing a fractional calculus into the observer design, the developed fractional order observers guarantee the estimated states reach the original system states. Using the fractional order Lyapunov approach, the stability (zer...

Abstract In this study, some new Lyapunov-type inequalities are presented for Caputo-Hadamard fractional Langevin-type equations of the forms $$ \begin{aligned} &amp;{}_{H}^{C}D_{a + }^{\beta } \bigl({}_{H}^{C}D_{a }^{\alpha }+ p(t)\bigr)x(t) q(t)x(t) = 0,\quad 0 &lt; a t b, \end{aligned} <mml...

This article is concerned with the global [Formula: see text] stabilization for a class of fractional-order memristive neural networks with time delays (FMDNNs). Two kinds of control scheme (i.e., state feedback control law and output feedback control law) are employed to stabilize a class of FMDNNs. Several stabilization conditions in form of algebraic criteria are presented based on a new fra...

In this paper, the synchronization problem of fractional-order complex-valued neural networks with discrete and distributed delays is investigated. Based on the adaptive control and Lyapunov function theory, some sufficient conditions are derived to ensure the states of two fractional-order complex-valued neural networks with discrete and distributed delays achieve complete synchronization rapi...

In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Ly...

In this paper, a novel fractional-order hyper-chaotic system is proposed. By drawing the phase trajectory and Lyapunov exponent spectrum, its dynamic characteristics are analyzed. The simulation results show that the fractional-order hyper-chaotic system has hyper-chaotic characteristic. Then, image encryption implementation based on the fractional-order hyper-chaotic system is investigated. An...