Fractional generalized synchronization in a class of nonlinear fractional order systems

Generalized synchronization in nonlinear fractional order systems occurs whether the states of one system by means of a functional mapping are identical to states of another. This mapping can be obtained if there exists a fractional differential primitive element whose elements are fractional derivatives which generate a differential transcendence basis. In this contribution we investigate the fractional generalized synchronization (FGS) problem for a class of strictly different nonlinear fractional order systems and we consider the master-slave synchronization scheme. As well as, of a natural manner we construct a fractional generalized observability canonical form, we introduce a fractional algebraic observability property, and we design a fractional dynamical controller able to achieve synchronization. These particular forms of FGS are illustrated with numerical results.