This paper proposes a current-controlled fractional-order memristor emulator based on one active building block. The emulator consists of a multiplication mode current conveyor (MMCC) block with three passive elements. Additionally, the series connection of fractional-order inductor (FOI) and fractional-order capacitor (FOC) with memristive elements in the i-v plane is demonstrated numerically for different cases. Changing the order of the FOC or FOI and its effect on the pinched hysteresis loop area are investigated, which improve the controllability of the double loop area, the location of the pinched point, and the operating frequency range. Numerical, PSPICE simulation results, and experimental verification are investigated for different cases to approve the theoretical findings. Moreover, a sensitivity analysis using Monte Carlo simulations for the tolerance of the discrete components of the memristor emulator is investigated. © 2020 IEEE.
A Universal Fractional-Order Memelement Emulation Circuit
This paper proposes a current-/voltage-controlled universal emulator that can realize any fractional-order memelements (FOME). The proposed emulator consists of second-generation current conveyors (CCII) block, two switches, and a multiplier/divider block. The first switch controls the emulator mode (voltage or current), while, the other controls the type of the emulated FOME. The influence of the fractional-order capacitor (FOC) on the pinched hysteresis loop (PHL) area, is discussed which increases the controllability on the double loop area and the working frequency range. Numerical and PSPICE simulations are presented for selected cases to prove the theoretical findings. © 2019 IEEE.
Image encryption in the fractional-order domain
This paper presents a new image encryption scheme based on the fractional-order Lorenz system which gives more degrees of freedom in key generation. In the modified fractional-order system, the key length is doubled using the three fractional-orde r parameters beside the three initial conditions, which makes it invulnerable to brute-force attacks. In addition, using a very simple algorithm, based on pixel confusion only, strongly encrypted images are produced. Such an algorithm can be used in real time applications. To evaluate the algorithm and analyze the encryption results, a standard image is used. A comparison of the colored correlation coefficients (horizontal, vertical, diagonal) for different cases with respect to a fractional-order parameter and another system parameter are introduced. Moreover, the encrypted image shows high sensitivity to the fractional-order key, which appears from the wrong decryption with 0.1% change of the fractional-order parameter. © 2012 IEEE.
Frational Order Inverse Filters Based on CCII Family
This paper proposes two generalized topologies of fractional order inverse filters (FOIF). All possible realizations of each topology are investigated using the second generation current conveyor (CCII) family. Inverse fractional highpass (IFHPF), inverse fractional bandpass (IFBPF), and inverse fractional lowpass (IFLPF) filters are realized using the same topology based on the generalized admittances. Numerical and P-Spice simulation results are presented for selected cases to approve the theoretical findings. The fractional order parameters increase the design flexibility and controllability which is validated experimentally. © 2019 IEEE.
Dynamics of fractional and double-humped logistic maps versus the conventional one
This paper presents the dynamic analysis of two discrete logistic chaotic maps versus the conventional map. The first map is the fractional logistic map with the extra degrees of freedom provided by the added number of variables. It has two more variables over the conventional one. The second map is the double-humped logistic map. It is a fourth-order map which increases the non-linearity over the conventional one. The dynamics of the three maps are discussed in details, including mathematical derivations of fixed points, stability analysis, bifurcation diagrams and the study of their chaotic regions. The chaotic behavior of the three maps, is investigated using the Maximum Lyapunov exponent (MLE). © 2017 IEEE.
Two topologies of fractional-order oscillators based on CFOA and RC networks
This paper presents two general topologies of fractional order oscillators. They employ Current Feedback Op-Amp (CFOA) and RC networks. Two RC networks are investigated for each presented topology. The general oscillation frequency, condition and the phase difference between the oscillatory outputs are investigated in terms of the fractional order parameters. Numerical simulations and P-Spice simulation results are provided for some cases to validate the theoretical findings. The fractional order parameters increase the design flexibility and controllability which is proved by the provided experimental results. © 2018 IEEE.
Generalized family of fractional-order oscillators based on single CFOA and RC network
This paper presents a generalized family of fractional-order oscillators based on single CFOA and RC network. Five RC networks are investigated with their general state matrix, and design equations. The general oscillation frequency, condition and the phase difference between the oscillatory outputs are introduced in terms of the fractional order parameters. They add extra degrees of freedom which in turn increase the design flexibility and controllability that is proved numerically. Spice simulations are introduced to validate the theoretical findings. © 2017 IEEE.
Tunable fractional-order band-pass filter of order 2?
In this work, a novel implementation of a tunable fractional-order bandpass filter of order 2? is proposed. The transfer function of the presented filter is approximated using the second-order Continued Fraction Expansion (CFE) approximation technique. The filter transfer function is realized using the Inverse Follow the Leader Feedback (IFLF) structure. The Operational Transconductance Amplifiers (OTAs) are used to implement the filter circuit. Furthermore, the proposed filter is tunable by varying the value of only one bias current, which adjust the value of ?. The simulations are performed using Matlab and Cadence software with UMC 0.13? m CMOS technology. © 2019 IEEE.
Generalized ?+?-order Filter Based on Single CCII
Different generalized filters topologies are proposed in the fractional-order domain. Three voltage-mode topologies and one current-mode topology are used to realize several types of fractional-order filters by applying different admittances combinations. The proposed topologies are designed using a single second-generation current conveyor (CCII-) and two fractional-order capacitors, which add more degrees of freedom for the design. The generalized Fractional Transfer Function (FTF) for each proposed topology is investigated where the fractional-order low-pass, band-pass, high-pass, and notch filters with ?+?)-order are realized. The Numerical results are provided where the stability analysis is presented for different cases. Also, the PSPICE simulations are presented to prove the theoretical findings of selected cases. © 2020 IEEE.
Low pass filter design based on fractional power chebyshev polynomial
This paper introduces the design procedure for the low pass filter based on Chebyschev polynomials of fractional power of any order. The filter order is considered in intervals of width two. Only the first two intervals are considered along with their pole locus produced by varying the filter order and the magnitude response. A general formula for constructing the filter from its s-plane poles is suggested. Numerical analysis and circuit simulations using MATLAB and Advanced Design System (ADS) based on the proposed design procedure are presented. Good matching between the circuit simulation and the numerical analysis is obtained which proves the reliability of the proposed design procedure. © 2015 IEEE.