Fractional-order calculus is the branch of mathematics which deals with non-integerorder differentiation and integration. Fractional calculus has recently found its way to engineering applications; particularly electronic circuits with promising results showing the feasibility of fabricating fractional-order capacitors on silicon. Fractionalorder capacitors are lossy non-deal capacitors with an impedance given by Zc = (1/j?C)?, where C is the pseudo-capacitance and ? is its order (0 < ? ? 1). When these fractional-order capacitors are employed within an oscillator (sinusoidal or relaxation) circuit, this oscillator is called a fractional-order oscillator and is described by non-integer-order differential equations. Therefore, an oscillator of order 1.5 or 2.6 is possible to obtain. While the oscillation frequency in integer-order oscillators is related to their RC time constants, fractional-order oscillators have their oscillation frequencies also related to ?. This adds more design freedom and enables extremely high or extremely low oscillation frequencies even with large RC time constants. This chapter aims at reviewing the theory of designing fractional-order oscillators accompanied by several design examples. Experimental results are also shown. © The Institution of Engineering and Technology 2017. All rights reserved.
Partial fraction expansion–based realizations of fractional-order differentiators and integrators using active filters
Approximations of the fractional-order differentiator and integrator operators s±r are proposed in this work
Low-voltage commercial super-capacitor response to periodic linear-with-time current excitation: A case study
The response of a commercial super-capacitor to an applied periodic current excitation in the form of a triangular waveform is investigated in this study
Review of fractional-order electrical characterization of supercapacitors
2018Abdelkareem M.A.Allagui A.Elwakil A.S.Fouda M.E.Freeborn T.J.JournalMaundy B.J.Radwan A.G.Said Z.
The tests and calculation of the key performance metrics of supercapacitors including capacitance, power and energy stored are commonly reported by the academia and the industry based on formulæ valid only for ideal capacitors
Fractional-Order Two-Port Networks
We introduce the concept of fractional-order two-port networks with particular focus on impedance and admittance parameters
Approximation of the fractional-order laplacian S? as a weighted sum of first-order high-pass filters
A new approximation method of the fractional-order Laplacian operator s? is introduced