Generalized Synchronization in chaotic Liouvillian fractional systems

In this paper the problem of generalized synchronization, is studied for chaotic Liouvillian nonlinear fractional systems of commensurate order. We propose a new fractional generalized observability canonical form (FGOCF) for a class of fractional nonlinear systems. The FGOCF is obtained through a coordinate transformation whose first element is the fractional integral of available output namely fractional differential primitive element. Further it is designed a fractional dynamical control law to achieve generalized synchronization for systems expressed in the FGOCF and for systems in original coordinates. Finally, the effectiveness of the proposed synchronization methodology for Liouvillian systems is verified by means of numerical results.