There are many dynamic systems that can be characterized better by using non-integer order dynamic model based on fractional calculus or, differentiation or integration. Traditional calculus is based on integer order differentiation and integration. In this paper, we have represented comparative study of different fractional order systems using different realization methods. Basic definitions of fractional calculus and fractional order dynamic systems are presented first. Additionally, different fractional order systems are introduced and commented. Numerical methods for simulating fractional order systems are given in detail. Also Discretization techniques for fractional order operators are explained in details. Both digital and analog realization methods of fractional order systems are introduced. Comparative study has been carried out for the time response analysis of fractional order system using various approximation methods. Finally, remarks on future research efforts in fractional order control are given.
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