Influence of the electrical parameters on the input impedance of a fractal structure realised on silicon

The Effect of Fractional Orders on the Transmission Power and Efficiency of Fractional-Order Wireless Power Transmission System

“…In the 19th century, the logic definitions of fractional calculus were proposed by Liouville in 1834, Riemann in 1847, Grünwald in 1867, and Caputo in 1967 [2][3][4][5], and the theoretical system of fractional calculus was gradually perfected. In recent years, fractional calculus has been widely investigated and applied to the modeling of many real phenomenon or actual systems, such as super capacitor [6], skin effect of the inductor [7], and fractal structures [8]. Besides, the concept of fractional order has been used in many areas such as physics, environmental hydraulics, biomedical applications, automatic control theory, electromagnetics, electrical circuits, and chaotic systems, etc.…”

Fractional‐order mutual inductance: analysis and design

“…This added flexibility is mainly due to the fact that fractional‐order systems can be characterized by infinite memory, whereas integer‐order systems are characterized by finite memory . Moreover, because of the extra fractional‐order parameters, more flexibility is added in the modeling, analysis, and control of many applications 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 and oscillators . Furthermore, applications of fractional calculus have been reported in many areas such as physics , nonlinear oscillation of earthquakes , and mathematical biology .…”

“…Therefore, it becomes possible to define a general fractance device with impedance proportional to s α , where the traditional circuit elements—capacitor, resistor, and inductor—are special cases of this fractional‐order element when the order is − 1, 0, and 1, respectively. During the last 10 years, several promising trials have been introduced for the realizations of the fractional element and based on different techniques such as chemical reactions , fractal shapes , and graphene material . Moreover, many finite circuit approximations were suggested to model fractional‐order elements, for example, a finite element approximation of the special case Z = 1/( Cs 0.5 ) was reported in .…”

An ultra-broadband single-component fractional-order capacitor using MoS2-ferroelectric polymer composite

“…It is important to mention here that, previously developed FOCs do not only suffer from narrow CPZs but also have other shortcomings that limit their use in modern electronic devices and systems. For instance, liquid electrode based (LEB) FOCs cannot be integrated with microelectronics, 6 the CPA of fractal tree (FT) FOCs cannot be tuned, 11 the FOCs making use of operational trans-conductance amplifiers (OTAs) are power hungry, [47][48][49] and the CPA of the FOCs fabricated using carbon-ferroelectric polymer composites is very sensitive to the filler ratio of the carbon 1,3 and it has a low dynamic range. 46 On the other hand, the FOCs proposed in this work are fully compatible with PCBs, passive, and have a stable CPA over a broader frequency range.…”

“…[1][2][3][4][5][6][7][8][9][10][11] Thanks to the additional parameter, namely, the fractional order (see supplementary material Sec. S1 and Fig.…”