An additional degree of freedom is introduced to fractional-Fourier-transform systems by use of anamorphic optics. A different fractional Fourier order along the orthogonal principal directions is performed. Alaboratory experimental system shows preliminary results that demonstrate the proposed theory. Applications such as anamorphic fractional correlation and multiplexing in fractional domains...

Fractional calculus has become an increasingly popular tool for modeling the complex behaviors of physical systems from diverse domains. One of the key issues to apply fractional calculus to engineering problems is to achieve the parameter identification of fractional-order systems. A time-domain identification algorithm based on a genetic algorithm (GA) is proposed in this paper. The multi-var...

As it results from many research works, the majority of real dynamical objects are fractional-order systems, although in some types of systems the order is very close to integer order. Application of fractional-order models is more adequate for the description and analysis of real dynamical systems than integer-order models, because their total entropy is greater than in integer-order models wi...

Nature often presents complex dynamics, which cannot be explained by means of ordinary models. In this paper, we establish an approach to certain fractional dynamic systems using only deterministic arguments. The behavior of the trajectories of fractional non-linear autonomous systems around the corresponding critical points in the phase space is studied. In this work we arrive to several inter...

We, for the first time, investigate the basic behaviours of a chaotic switching fractional system via both theoretical and numerical ways. To deeply understand the mechanism of the chaos generation, we also analyse the parameterization of the switching fractional system and the dynamics of the system’s trajectory. Then we try to write down some detailed rules for designing chaotic or chaos-like...

We propose second-order implicit-explicit (IMEX) time-stepping schemes for nonlinear fractional differential equations with fractional order 0 < β < 1. From the known structure of the nonsmooth solution and by introducing corresponding correction terms, we can obtain uniformly second-order accuracy from these schemes. We prove the convergence and linear stability of the proposed schemes. Numeri...

The unstable equilibrium points of the fractional-order Lorenz chaotic system can be controlled via fractional-order derivative, and chaos synchronization for the fractional-order Lorenz chaotic system can be achieved via fractional-order derivative. The control and synchronization technique, based on stability theory of fractional-order systems, is simple and theoretically rigorous. The numeri...

Control and synchronization of the financial systems with fractional-order are discussed in this paper. Based on the stability theory of fractional-order differential equations, Routh-Hurwitz stability condition, and by using linear control, simpler controllers are designed to achieve control and synchronization of the fractional-order financial systems. The proposed controllers are linear and ...

Fractional-order financial system introduced by W.-C. Chen 2008 displays chaotic motions at order less than 3. In this paper we have extended the nonlinear feedback control in ODE systems to fractional-order systems, in order to eliminate the chaotic behavior. The results are proved analytically by applying the Lyapunov linearization method and stability condition for fractional system. Moreove...