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This study investigates the use of fractional order differential models tosimulate the dynamic response of non-homogeneous discrete systems and toachieve efficient and accurate model order reduction. The traditional integerorder approach to the simulation of non-homogeneous systems dictates the use ofnumerical solutions and often imposes stringent compromises between accuracyand computational performance. Fractional calculus provides an alternativeapproach where complex dynamical systems can be modeled with compact fractionalequations that not only can still guarantee analytical solutions, but can alsoenable high levels of order reduction without compromising on accuracy.Different approaches are explored in order to transform the integer order modelinto a reduced order fractional model able to match the dynamic response of theinitial system. Analytical and numerical results show that, under certainconditions, an exact match is possible and the resulting fractionaldifferential models have both a complex and frequency-dependent order of thedifferential operator. The implications of this type of approach for both modelorder reduction and model synthesis are discussed.

Model-order reduction of lumped parameter systems via fractional calculus