Nowadays, impedance converter and inverter circuits are very vital for the fractional order circuit design. Mutators are one of the common circuits used for that purpose. So, two fractional order mutators are discussed in this work; the first one converts a resistance into a fractional order element. The second mutator family converts any fractional order element to a different fractional order element. Circuit simulations for the mutator circuits using Advanced Design System (ADS) are performed and proved that the circuits are able to achieve the required phase response. © 2016 IEEE.

In this paper, the effect of non-zero initial condition on the time domain responses of fractional-order systems using Caputo and Riemann-Liouville (RL) fractional definitions are discussed. Analytical formulas were derived for the step and square wave responses of fractional-order RCα circuit under RL and Caputo operators for non-zero initial condition. Moreover, a simulation scheme for fractional state-space systems with non-zero initial condition is introduced. © 2016 IEEE.

The book reports on the latest advances in and applications of fractional order control and synchronization of chaotic systems, explaining the concepts involved in a clear, matter-of-fact style. It consists of 30 original contributions written by eminent scientists and active researchers in the field that address theories, methods and applications in a number of research areas related to fractional order control and synchronization of chaotic systems, such as: fractional chaotic systems, hyperchaotic systems, complex systems, fractional order discrete chaotic systems, chaos control, chaos

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Two novel nonlinear circuits that exhibit an all-positive pinched hysteresis loop are proposed. These circuits employ two NMOS transistors, one of which operates in its triode region, in addition to two first-order filter sections. We show the equivalency to a charge-controlled resistance (memristance) in a decremental state via detailed analysis. Simulation and experimental results verify the proposed theory. © 2017 B. J. Maundy et al.

A fractional-order circuit model is explored to represent the leakage/self-discharge behaviour of commercially available supercapacitors. This fractional order-model is composed of two elements, a fractional-order capacitor with impedance Z = 1/CαSα and a parallel resistance Rp, which set the discharge based on the time constant τ = (RpC)1/α and order α. Self-discharging data was collected from a 3 F PowerStor, 1 F Panasonic, and 350 F Maxwell supercapacitors after being charged and left in a floating state while monitoring the device terminal voltage. The parameters for the fractional-order

Mathematical Techniques of Fractional Order Systems illustrates advances in linear and nonlinear fractional-order systems relating to many interdisciplinary applications, including biomedical, control, circuits, electromagnetics and security. The book covers the mathematical background and literature survey of fractional-order calculus and generalized fractional-order circuit theorems from different perspectives in design, analysis and realizations, nonlinear fractional-order circuits and systems, the fractional-order memristive circuits and systems in design, analysis, emulators, simulation

Recently, double pinch-off points have been discovered in some memristive devices where the I-V hysteresis curve intersects in two points generating triple lobes. This paper investigates a fractional-order flux-controlled mathematical model which is able to develop the multiple pinch-off points or multiple lobes. The conditions for observing double pinch-off points (triple lobes) are derived in addition to the locations of the pinch-off points which do not appear in the integer domain. Also, expressions for maximum and minimum conductance are derived. Finally, a floating fractional flux

Random bit generators (RBGs) in today's digital information and communication systems employ a high rate physical entropy sources such as electronic, photonic, or thermal time series signals. However, the proper functioning of such physical systems is bound by specific constrains that make them in some cases weak and susceptible to external attacks. In this study, we show that the electrical current time series of contact glow discharge electrolysis, which is a dc voltage-powered micro-plasma in liquids, can be used for generating random bit sequences in a wide range of high dc voltages. The

Shared by various physical, chemical, and biological systems, fractional-order dynamics assert that the present state of a system is the result of not only the applied stimulus but also its past history. Consequently, in fractional-order systems, there exists a system-specific, input-dependent memory kernel. In this study, we demonstrate experimentally the existence of a memory effect in electric double-layer capacitors which are known to exhibit a fractional-order behavior through their non-single, distributed internal time constants. This is performed by showing variance in the discharge