2017
DOI: 10.1007/s41403-017-0020-1
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Realization of Fractional Order Elements

Abstract: 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 c… Show more

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Cited by 33 publications
(15 citation statements)
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“…In the analog realization domain, there are also approximate implementations of fractional elements by using discrete active and passive elements such as RC or RL ladder structures [188]- [193]. A brief survey of FO element realizations in term of multicomponent and single component solutions was presented in [194]. These works clearly demonstrate that a fractional-order circuit design using fractional-order passive elements can be a realistic solution for analog FOPID controllers.…”
Section: Maximum and Minimum Values Of Test Resultsmentioning
confidence: 99%
“…In the analog realization domain, there are also approximate implementations of fractional elements by using discrete active and passive elements such as RC or RL ladder structures [188]- [193]. A brief survey of FO element realizations in term of multicomponent and single component solutions was presented in [194]. These works clearly demonstrate that a fractional-order circuit design using fractional-order passive elements can be a realistic solution for analog FOPID controllers.…”
Section: Maximum and Minimum Values Of Test Resultsmentioning
confidence: 99%
“…As such the mathematical expressions for capacitors shall include the fractional-operator. Fractional-order models have indeed been provided for supercapacitors by various researchers [2,5].…”
Section: A Non-ideal Capacitor -Fractional-order Capacitormentioning
confidence: 99%
“…Besides its applications in several fields, a variety of electrical circuits like filters, oscillators, neural circuits, transmission lines, supercapacitors, batteries, PID controllers, square and cube rooting circuits, resonators, sensing circuits etc. have also been modified with the use of fractional-order calculus [1][2][3][4][5][6][7]. However, the electrical implementation of fractional-order calculus requires the realization of electrical components that follow the laws of such non-integer order calculus.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…2527 Adhikary et al. 29 reviewed some significant research work, along with their success and limitations, in the field of fractional circuit realization.…”
Section: Introductionmentioning
confidence: 99%