Fractional-Order Circuits and Systems: An Emerging Interdisciplinary Research Area

Elwakil, Ahmed S.

doi:10.1109/mcas.2010.938637

Cited by 502 publications

(242 citation statements)

References 69 publications

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“…Owing to the interdisciplinary nature of the fractional calculus, 1 there is a growing research interest in the development of fractional-order circuits including¯lters, [2][3][4][5][6][7][8][9] oscillators, [10][11][12][13] biological tissues emulators, 14 and energy storage devices. 15 In these applications, the basic building blocks are the fractional-order capacitors and/or fractional-order inductors.…”

Section: Introductionmentioning

confidence: 99%

Comparative Study of Discrete Component Realizations of Fractional-Order Capacitor and Inductor Active Emulators

Τσιριμώκου

Kartci

Koton

et al. 2018

J CIRCUIT SYST COMP

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Due to the absence of commercially available fractional-order capacitors and inductors, their implementation can be performed using fractional-order di®erentiators and integrators, respectively, combined with a voltage-to-current conversion stage. The transfer function of fractional-order di®erentiators and integrators can be approximated through the utilization of appropriate integer-order transfer functions. In order to achieve that, the Continued Fraction Expansion as well as the Oustaloup's approximations can be utilized. The accuracy, in terms of magnitude and phase response, of transfer functions of di®erentiators/integrators derived through the employment of the aforementioned approximations, is very important factor for achieving high performance approximation of the fractional-order elements. A comparative study of the accuracy o®ered by the Continued Fraction Expansion and the Oustaloup's approximation is performed in this paper. As a next step, the corresponding implementations of the emulators of the fractional-order elements, derived using fundamental active cells such as operational ampli¯ers, operational transconductance ampli¯ers, current conveyors, and current feedback operational ampli¯ers realized in commercially available discrete-component IC form,

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Section: Introductionmentioning

confidence: 99%

Comparative Study of Discrete Component Realizations of Fractional-Order Capacitor and Inductor Active Emulators

Τσιριμώκου

Kartci

Koton

et al. 2018

J CIRCUIT SYST COMP

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“…Recently, the realization and generalization of fractional calculus has become of great significance in many fields [1] such as determining voltage-current relationship in a non-ideal capacitor, fractal behavior of a metal insulator solution interface, electromagnetic waves, and recently in electrical circuits such as filters [2]- [7], oscillators [8] [9] [10], passive realization [11] [12] and energy-related issues in supercapacitors [13]. Furthermore, applications of fractional calculus have been reported in many areas such as physics [14], nonlinear oscillation of earthquakes [15], and mathematical biology [16].…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic Interpretation of Fractional-Order Elements

Liang¹,

Hao²,

Shan³

2017

JMP

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Fractional circuits have attracted extensive attention of scholars and researchers for their superior performance and potential applications. Recently, the fundamentals of the conventional circuit theory were extended to include the new generalized elements and fractional-order elements. As is known to all, circuit theory is a limiting special case of electromagnetic field theory and the characterization of classical circuit elements can be given an elegant electromagnetic interpretation. In this paper, considering fractional-order time derivatives, an electromagnetic field interpretation of fractional-order elements: fractional-order inductor, fractional-order capacitor and fractional-order mutual inductor is presented, in terms of a quasi-static expansion of the fractional Maxwell's equations. It shows that fractional-order elements can also be interpreted as a fractional electromagnetic system. As the element order equals to 1, the interpretation of fractional-order elements matches that of the classical circuit elements: L, C, and mutual inductor, respectively.

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“…For systems containing supercapacitors, these differences are mainly due to their electrochemical construction [8]. Besides supercapacitors, many new practical realizations of the fractional-order capacitor C α have been developed, among others using the equivalent RC ladder structures, some dielectrics (e.g., LiN 2 H 5 SO 4 ), fractal systems [4,14,27] and many others. For the description of lossy coils with soft ferromagnetic cores, fractional-order models have been used too [28,29].…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Transient State in a Series Circuit of the Class $$RL_{\beta }C_{\alpha }$$ R L β C α

Jakubowska¹,

Walczak²

2016

Circuits Syst Signal Process

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Results of analysis of transient states in a series circuit of the class RL β C α , supplied by an ideal voltage source, have been described in the paper. This circuit consists of a coil L β and a supercapacitor C α described by fractional-order differential equations. A method for determining the current and voltage waveforms in the analyzed circuit, based on the decomposition of rational functions into partial fractions, has been described. This method allows to determine transient waveform shapes in the system for any kind of voltage excitation. Two cases of the problem solutions have been considered. The first case concerns a situation where poles of rational functions are real, and the second where rational functions have complex poles. Effective relations enabling the determination of transient waveforms in a closed form have been given. Analytical formulae describing transient state waveforms in the system for different types of voltage excitations: constant, monoharmonic, periodic and arbitrary being an element of a Hilbert space, have been determined, too. The obtained results have been illustrated by an example.

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Fractional-Order Circuits and Systems: An Emerging Interdisciplinary Research Area

Cited by 502 publications

References 69 publications

Comparative Study of Discrete Component Realizations of Fractional-Order Capacitor and Inductor Active Emulators

Comparative Study of Discrete Component Realizations of Fractional-Order Capacitor and Inductor Active Emulators

Electromagnetic Interpretation of Fractional-Order Elements

Analysis of the Transient State in a Series Circuit of the Class $$RL_{\beta }C_{\alpha }$$ R L β C α

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