A survey of single and multi-component Fractional-Order Elements (FOEs) and their applications

Analysis of Disordered Dynamics in Polymer Nanocomposite Dielectrics for the Realization of Fractional-Order Capacitor

“…THE wide application of fractional-order calculus in designing system dynamics and in modeling natural and manmade phenomenon has interested several researchers in the recent past [1,2]. The reason being the availability of extra degree of freedom in terms of the fractional-order and also that this approach incorporates memory effect [2,3].…”

FPAA-based implementation of fractional-order chaotic oscillators using first-order active filter blocks

“…The FPAA includes analog blocks to synthesize filters and also includes multipliers and amplifiers. The FPAA can be used for fast verification of a fractional-order dynamical system, and in a further step those blocks can be designed using integrated circuit technology, as it was done in designing fractional-order filters [8] , and fractional-order elements [9] . However, the possibility of success when using an FPAA, depends on the number of analog blocks that are required to implement a fractional-order dynamical system, which is a challenge as a problem to reduce the number of amplifiers in a FOCO.…”

Synthesis of elements with fractional-order impedance based on homogenous distributed resistive-capacitive structures and genetic algorithm

“…Elements with fractional-order impedance (EFI) also known as fractional-order elements (FOEs) [1] or simply fractors [2] are very perspective building blocks for non-integer (i.e. fractional) order circuits and systems.…”

“…The recent survey on possible techniques and approaches to design single or multi-component FO capacitors as being proposed by different research groups can be found in [1] . Here the authors state that particularly single-component EFIs are being researched upon vigorously.…”

“…Common features of these elements are low range of the fractional order α and/or narrow frequency band of the constant phase shift. None of the elements is currently commercially available in the solid-state form and most of them also do not have any dependence relation between the order α and the electrochemical parameters [1] .…”