in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...

In this paper, a sliding mode control law is designed to control chaos in a class of fractional order new Lorenz-like chaotic systems. By using the sliding mode control method, the states of the fractional-order system have been stabled, even if the system with uncertainty is in the presence of external disturbance. The stability of the corresponding equilibria is also argued similarly to the i...

In this paper, we consider the pinning control problem of fractional-order weighted complex dynamical networks. The well-studied integer-order complex networks are the special cases of the fractional-order ones. The network model considered can represent both directed and undirected weighted networks. First, based on the eigenvalue analysis and fractional-order stability theory, some local stab...

This paper deals with the design of Fractional Order Proportional Integral (FO-PI) controller for the speed control of DC motor. A mathematical model of DC motor control system is derived and based on this model fractional order PI controller is designed using stability boundary locus method to satisfy required gain margin (GM) and phase margin (PM) of the system. Servo and Regulatory tracking ...

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...

In this work, the authors investigate the stability conditions in a fractional-order financial system using the fractional Routh-Hurwitz criteria. According to the qualitative theory, the existence and uniqueness of solutions for a class of commensurate fractional-order financial systems are investigated. A necessary condition for this system to remain chaotic is obtained. It is found that chao...

In this paper we introduce the different types of the Fractional Order PID controllers and presented some of its application to Industry and robotics Key-Words: Fractional Order Calculus, Differintegration, Fractional Order Controllers, Control Theory, Control Systems, PID controller, tuning, auto-tuning.