  This study investigates the use of fractional order differential models to
simulate the dynamic response of non-homogeneous discrete systems and to
achieve efficient and accurate model order reduction. The traditional integer
order approach to the simulation of non-homogeneous systems dictates the use of
numerical solutions and often imposes stringent compromises between accuracy
and computational performance. Fractional calculus provides an alternative
approach where complex dynamical systems can be modeled with compact fractional
equations that not only can still guarantee analytical solutions, but can also
enable high levels of order reduction without compromising on accuracy.
Different approaches are explored in order to transform the integer order model
into a reduced order fractional model able to match the dynamic response of the
initial system. Analytical and numerical results show that, under certain
conditions, an exact match is possible and the resulting fractional
differential models have both a complex and frequency-dependent order of the
differential operator. The implications of this type of approach for both model
order reduction and model synthesis are discussed.
