In this paper, a projective synchronization approach for a class of fractional-order chaotic systems with fractional-order 1 < q < 2 is demonstrated. The projective synchronization approach is established through precise theorization. To illustrate the effectiveness of the proposed scheme, we discuss two examples: (1) the fractional-order Lorenz chaotic system with fractional-order q = 1.1; (2)...

The Liouville equation, first Bogoliubov hierarchy and Vlasov equations with derivatives of non-integer order are derived. Liouville equation with fractional derivatives is obtained from the conservation of probability in a fractional volume element. This equation is used to obtain Bogoliubov hierarchy and fractional kinetic equations with fractional derivatives. Statistical mechanics of fracti...

In this paper, we discuss in time domain the convergence of the iterative process for fractional-order systems. Fractional order iterative learning updating schemes are considered. The convergent conditions of the fractional-order and integer-order iterative learning schemes are proved to be equivalent. It is shown in Matlab/Simulink results that the tracking speed is the fastest when the syste...

In positive systems inputs, state variables and outputs take only non-negative values. Examples of positive systems are industrial processes involving chemical reactors, heat exchangers and distillation columns, storage systems, compartmental systems, water and atmospheric pollution models. A variety of models having positive linear behavior can be found in engineering, management science, econ...

Descriptor (singular) linear systems have been considered in many papers and books (Bru et al., 2003; 2002; Choundhury, 1972; Campbell et al., 1976; Dai, 1989; Guang-Ren Duan, 2010; Kaczorek, 2013; 2011a; 2014b; 2004; 1992; 2014c; 2011c; 2011d; 2011e; Virnik, 2008). The eigenvalue and invariant assignment by state and output feedbacks was investigated by Kaczorek (2004; 2011d), along with minim...

The aim of this paper is to present a modified explanation of the classic internal model principle for certain class of finite-dimensional, time-invariant, deterministic fractionalorder systems commonly known as fractional systems of commensurate order. The necessary and sufficient conditions for perfect command tracking and disturbance rejection are provided. The difficulty of applying the cla...

In this paper, Backstepping method is proposed to synchronize two fractional-order systems. The simulation results show that this method can effectively synchronize two chaotic systems. Keywords—Backstepping method, Fractional order, Synchronization.

Keywords: Fractional-order linear systems Interval uncertainty Necessary and sufficient stability condition a b s t r a c t This paper establishes a necessary and sufficient stability condition of fractional-order interval linear systems. It is supposed that the system matrix A is an interval uncertain matrix and fractional commensurate order belongs to 1 ≤ α < 2. Using the existence condition ...

This paper presents the Euler–Lagrange equations for fractional variational problems with multiple integrals. The fractional Noether-type theorem for conservative and nonconservative generalized physical systems is proved. Our approach uses well-known notion of the RiemannLiouville fractional derivative.