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The concept of model order reduction of high integer order systems using approximate moment matching has been generalized and extended to rational approximation of fractional order transfer function (FOTF). This approximation method converts an FOTF into characteristic numeric values and thus can be applied to rational approximation of FOTF, irrespective of its form of representation. This is very effective when FOTF has multiple fractional powered terms. Two circuit configurations for analog realization of FOTF through rational approximation are discussed and have been shown to be useful in hardware implementation. As a case study, a half order differentiator has been implemented in hardware and can be extended to any FOTF.

A fractor or a fractional order element should show a constant phase (CP), between ±90 0 (except 0 0 ) at any frequency, theoretically. However, all the practical realization of single component fractor have limitation in their CP zone. Not many single-component-fractors have been reported having CP zone more than a decade. In this work, new electrochemical type fractors have been developed, by coating a polymer-carbon nanotube (CNT) composite over Cu clad epoxy block and putting the block in polarizing solution. By varying the percentage of CNT in polymer-CNT composite and the nature of polarizing solution, two different types of fractor have been realized. One is a wide -band fractor having CP zone of five decades (20 Hz to 2 MHz) with a ripple of ±2 0 only. The other one shows two distinct CP zones at two different phase angles. Each zone is about two decade long. These fractors will help to realize fractional order circuits which need to be operated in wide frequency band.

Fractional order (FO) element (FOE) is the building block for realization of FO systems, an important research domain. However, the realization of FO system is still a challenge. Till date, no FOE or fractor is available in the market. However, many researchers have developed various types of FOE, multi-component and single component, over past 50 years or more. This paper reviews some significant research work, along with their success and limitations, in the field of FOE realization. Also, it discusses the chronological development and a brief comparative study to present an overall idea on current stage of FOE research to the readers.

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