We study the existence and approximate controllability of a class of fractional nonlocal delay semilinear differential systems in a Hilbert space. The results are obtained by using semigroup theory, fractional calculus, and Schauder’s fixed point theorem. Multi-delay controls and a fractional nonlocal condition are introduced. Furthermore, we present an appropriate set of sufficient conditions ...

Projective synchronization between two different fractional-order chaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the stability theory of fractional-order differential equations, a suitable and effective adaptive control law and a parameter update rule for unknown parameters are designed, such that projective synchronization between ...

In this work, a fractional chaotic system is introduced, where the capacitor and the inductor of the original circuit are replaced by a fractional electric element called fractance. Moreover, a feedback nonlinear controller is designated and used both to control chaos in this fractional system to its unstable (equilibriums or periodic orbits) and to achieve identical synchronization. Furthermor...

Fractional calculus is about the integration or differentiation of non-integer orders. The use of “fractional” is purely due to historical reasons [1]. Using fractional order differential equations is believed to be able to better characterize the nature around us. Using an integer order model is only for our own convenience. Depending on the scale on which we characterize the dynamics of a sys...

This paper addresses the use of fractional order control (FOC) in the context of control through networks to minimize or compensate the effect of the time-varying networkinduced delay. In particular, two fractional order strategies are presented based on the adaptation of, on one hand, the gains of a fractional order PI controller, and, on the other hand, both its gains and its order in accorda...

The aim of this paper is to employ fractional order proportional integral derivative (FO-PID) controller and integer order PID controller to control the position of the levitated object in a magnetic levitation system (MLS), which is inherently nonlinear and unstable system. The proposal is to deploy discrete optimal pole-zero approximation method for realization of digital fractional order con...

We construct for the first time a fractional-order hyperchaotic system via original integer-order system. The dynamical behavior of this is investigated in detail using approximation method and Lyapunov exponents. Next, an adaptive control strategy univariate controlled has been proposed. Also, tracking performance fully taken into account numerous applications, instance, sinusoidal periodic si...

Based on linear feedback control technique, a projective synchronization scheme ofN-dimensional chaotic fractional-order systems is proposed, which consists of master and slave fractional-order financial systems coupled by linear state error variables. It is shown that the slave system can be projectively synchronized with the master system constructed by state transformation. Based on the stab...