Passive Realization of Fractional-Order Impedances by a Fractional Element and RLC Components: Conditions and Procedure

Power Laws in Fractionally Electronic Elements

“…c (t) denotes the fractional derivative of order α of u c [1]. One calls C f the pseudo-capacitance of a capacitor because its unit is Farad × s 1−α instead of Farad [1]. In this article, we call it fractional capacitance of order α of a capacitor.…”

“…where u L and i L are the voltage and current over and through an inductor L with the constant inductance denoted again by L. The unit of L f is Henry × s 1−β . It is also called the pseudo-inductance [1,2]. Fractional elements, including a fractional capacitor and a fractional inductor, attract research interests in engineering.…”

“…Fractional elements, including a fractional capacitor and a fractional inductor, attract research interests in engineering. The literature about their analysis and applications is rich, see References [1][2][3][4][5][6][7][8][9][10], referring [11][12][13][14] to some recent work on fractional calculus. However, reports about power laws that fractional elements follow are rarely seen.…”

Electromagnetic Interpretation of Fractional-Order Elements

“…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].…”

Towards fractional-order capacitors with broad tunable constant phase angles: multi-walled carbon nanotube-polymer composite as a case study

“…high power consumption, and high fabrication cost [18][19][20][21][22][23][24][25] under continuous stirring for another 24 hours. It should be noted here that the minimum wt % is selected to be 1.00 20 since it has been reported previously that the percolation starts for values of wt% higher than 0.75 [10].…”