On the controllability of fractional dynamical systems

In the last three decades, interest in fractional calculus has experienced rapid growth and at present we can find many papers devoted its theoretical and application aspects (see the work of Machado et al. (2011) and the references therein). Fractional order models of real systems are often more adequate than the usually used integer order models in electrochemistry (Ichise et al., 1971), advection dispersion models (Benson et al., 2000), anomalous diffusion (Metzler and Klafter, 2000), viscoelastic materials (Renardy et al., 1987), fractal networks (Al Akaidi, 2004; Arena et al., 2000; West et al., 2003) and robotics (Valerio and Sa da Costa, 2004), etc. This is mainly due to the fact that the description of some systems is more accurate when the fractional derivative is used. For example, consider the time fractional advection– dispersion equation obtained by Liu et al. (2003) by replacing the time-derivative in the advection–dispersion equation by a generalized derivative of order α with 0 < α ≤ 1,