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Image enhancement is a vital process that serves as a tool for improving the quality of a lot of real-life applications. Fractional calculus can be utilized in enhancing images using fractional order kernels, adding more controllability to the system, due to the flexible choice of the fractional order parameter, which adds extra degrees of freedom. The proposed system merges two fractional order kernels which helps in image enhancement techniques, and the contribution of this work is based on the study of how to optimize this process. The optimization of the two fractional kernels was done using the neural network optimization algorithm (NNA) to utilize the best order for the two kernels. In this paper, three fractional kernels are studied to highlight the performance of image enhancement using fractional kernels against different metrics. Furthermore, three different combinations of two kernels are combined and studied to enhance the metrics score by utilizing two different fractional orders for each kernel. Various optimization algorithms are used to obtain the optimum fractional order for both single and combined kernels. Using the constrained NNA, the evaluation metrics of the image enhancement show a 33% increase in measure of enhancement metric (EME), 21% increase in contrast, and 4% increase in average gradient compared to the best-achieved metrics by the literature while keeping the similarity metric above 0.75. [ABSTRACT FROM AUTHOR]

This paper discusses the implementation sensitivity of chaotic systems added to their widely discussed sensitivities to initial conditions and parameter variation. This sensitivity can cause mismatches in some applications, which require an exact duplication of the system, e.g., chaos-based cryptography, synchronization and communication. Specifically, different implementation cases of three discretized jerk-based chaotic systems and a discrete-time logistic map are presented corresponding to different orders of additions and multiplications. The cases exhibit roughly similar attractor shapes, bifurcation behavior and Lyapunov exponents. However, mismatches between the time series corresponding to these cases in software double-precision, single-precision floating-point and hardware fixed-point implementations are reported. The number of time units after which the mismatch starts to become noticeable, and the effects of the discretization step and precision are discussed. Experimental results on Artix-7 XC7A100T FPGA and oscilloscope validate the presence of mismatch reported through simulations. The wrong decryption effect of this mismatch is demonstrated for a software image encryption application, where one case is used for encryption and the other(s) for decryption. Pseudo-Random Number Generation and image encryption application using the mismatch signal as a chaotic generator are proposed and show good results using several well-established performance metrics. [ABSTRACT FROM AUTHOR]

This paper introduces a fractional-order eardrum Type-II model, which is derived using fractional calculus to reduce the number of elements compared to its integer-order counterpart. The proposed fractional-order model parameters are extracted and compared using five meta-heuristic optimization techniques. The CMOS implementation of the model is performed using the Design Kit of the Austria Mikro Systeme (AMS) 0.35 μ m CMOS process, while the simulations have been performed using the Cadence IC design suite. [ABSTRACT FROM AUTHOR]

In this paper, three novel fractional-order CFOA-based inverse filters are introduced. The inverse low-pass, high-pass and band-pass responses are investigated using different approximation techniques. The studied approximations for the fractional-order Laplacian operator are the continued fraction expansion and Matsuda approximations. A comparison is held between the ideal filter characteristic and the realized ones from each approximation. A comparative study is summarized between the proposed circuits with some of the released inverse filters introduced in the literature. Foster-I realization is employed to transform the obtained fractional-order capacitor (FOC) from the investigated approximations into an RC parallel–series circuit topology. Additionally, to discuss the sensitivity of the FOC to component tolerances, Monte Carlo simulations are carried out which shows immunity to the component tolerances. Numerical examples, as well as SPICE circuit simulations, have been introduced to validate the theoretical discussions. Finally, the three CFOA inverse filters are tested experimentally. [ABSTRACT FROM AUTHOR]

This paper introduces all the possible topologies of the Wien bridge oscillator family. This family has 72 topologies, 24 of them contain only RC or RL pairs, and the rest contain mixed pairs. The complete mathematical analysis of all twelve possible capacitive-based topologies is proposed in the fractional-order domain. The investigated circuits can be categorized into two groups, each with a similar characteristic equation. Three integer-order approximation techniques for the Laplacian operator s α are employed to solve and simulate the Wien bridge system. The studied approximations are those of Matsuda, Oustaloup, and Valsa's network. Fractional-order capacitor (FOC) emulators are built using these approximations and applied in the circuit simulation. Comparisons are made on different levels, starting with the mathematical solution of the characteristic equation, followed by PSpice simulation, which compares topologies of the Wien bridge oscillator family. Hardware implementation of the FOC emulators is presented applying passive discrete components using the Foster-I technique. Additionally, sensitivity tests of the discrete components of the FOC emulators are performed using Monte Carlo analysis. Experimental results are introduced to validate the theoretical findings. [ABSTRACT FROM AUTHOR]

Having an approximate realization of the fractance device is an essential part of fractional-order filter design and implementation. This encouraged researchers to introduce many approximation techniques of fractional-order elements. In this paper, the fractional-order KHN low-pass and high-pass filters are investigated based on four different approximation techniques: Continued Fraction Expansion, Matsuda, Oustaloup, and Valsa. Fractional-order filter fundamentals are reviewed then a comparison is made between the ideal and actual characteristic of the filter realized with each approximation. Moreover, stability analysis and pole movement of the filter with respect to the transfer function parameters using the exact and approximated realizations are also investigated. Different MATLAB numerical simulations, as well as SPICE circuit results, have been introduced to validate the theoretical discussions. Also, to discuss the sensitivity of the responses to component tolerances, Monte Carlo simulations are carried out and the worst cases are summarized which show good immunity to component deviations. Finally, the KHN filter is tested experimentally. [ABSTRACT FROM AUTHOR]

A fractional-order capacitor and inductor emulator, implemented using MOS transistors, instead of passive capacitors, is introduced in this paper. This is achieved using current mirrors as active elements, without passive resistors, and therefore reducing the circuit complexity and resulting in both a resistorless and capacitorless topology. The emulator has been designed by combining fractional-order differentiator or integrator topologies with a voltage-to-current converter. An important benefit from the design flexibility point of view is that the same topology could be used for emulating a fractional-order capacitor or inductor through an appropriate selection of the time constants and gain factors. Considering that the MOS transistors operate in the strong inversion region, it is feasible for this emulator to operate at high frequencies. The evaluation of the proposed topology has been performed using Cadence IC design suite and the Design Kit provided by the Austrian Micro Systems 0.35 μm CMOS process. [ABSTRACT FROM AUTHOR]

This paper introduces the concept of fractional-order complex Chebyshev filter. A fractional variation of Chebyshev differential equations is introduced based on Caputo fractional operator. The proposed equation is solved using fractional Taylor power series method. The condition for fractional polynomial solutions is obtained and the first four polynomials scaled using an appropriate scaling factor. The fractional-order complex Chebyshev low-pass filter based on the obtained fractional polynomials is developed. Two methods for obtaining the transfer functions of the complex filter are discussed. Circuit implementations are simulated using Advanced Design System (ADS) and compared with MATLAB numerical simulation of the obtained transfer functions to prove the validity of the two approaches. [ABSTRACT FROM AUTHOR]

In this paper, a general analysis of the generation for all possible fractional order oscillators based on two-port network is presented. Three different two-port network classifications are used with three external single impedances, where two are fractional order capacitors and a resistor. Three possible impedance combinations for each classification are investigated, which give nine possible oscillators. The characteristic equation, oscillation frequency and condition for each presented topology are derived in terms of the transmission matrix elements and the fractional order parameters $$\alpha $$ and $$\beta $$ . Mapping between some cases is also illustrated based on similarity in the characteristic equation. The use of fractional order elements $$\alpha $$ and $$\beta $$ adds extra degrees of freedom, which increases the design flexibility and frequency band, and provides extra constraints on the phase difference. Study of four different active elements, such as voltage-controlled current source, gyrator, op-amp-based network, and second-generation current-conveyor-based network, serve as a two-port network is presented. The general analytical formulas of the oscillation frequency and condition as well as the phase difference between the two oscillatory outputs are derived and summarized in tables for each designed oscillator network. A comparison between fractional order oscillators with their integer order counterparts is also illustrated where some designs cannot work in the integer case. Numerical Spice simulations and experimental results are given to validate the presented analysis. [ABSTRACT FROM AUTHOR]

This paper presents three different optimization cases for normalized fractional order low-pass filters (LPFs) with numerical, circuit and experimental results. A multi-objective optimization technique is used for controlling some filter specifications, which are the transition bandwidth, the stop band frequency gain and the maximum allowable peak in the filter pass band. The extra degree of freedom provided by the fractional order parameter allows the full manipulation of the filter specifications to obtain the desired response required by any application. The proposed mathematical model is further applied to a case study of a practical second- generation current conveyor (CCII)-based fractional low-pass filter. Circuit simulations are performed for two different fractional order filters, with orders 1.6 and 3.6, with cutoff frequencies 200 and 500 Hz, respectively. Experimental results are also presented for LPF of 4.46 kHz cutoff frequency using a fabricated fractional capacitor of order 0.8, proving the validity of the proposed design approach. [ABSTRACT FROM AUTHOR]

An introduction is presented which discusses various topics within the issue including circuit theory of fractional-order circuits, oscillatory design and applications for fractional-order filters and applications of fractional-order circuits in renewable energy.

This paper discusses the boundary dynamics of the charge-controlled memcapacitor for Joglekar's window function that describes the nonlinearities of the memcapacitor's boundaries. A closed form solution for the memcapacitance is introduced for general doping factor $$p$$ . The derived formulas are used to predict the behavior of the memcapacitor under different voltage excitation sources showing a great matching with the circuit simulations. The effect of the doping factor $$ p$$ on the time domain response of the memcapacitor has been studied as compared to the linear model using the proposed formulas. Moreover, the generalized fundamentals such as the saturation time of the memcapacitor are introduced, which play an important role in many control applications. Then the boundary dynamics under sinusoidal excitation are used as a basis to analyze any periodic signal by Fourier series, and the results have been verified using PSPICE simulations showing a great matching. As an application, two configuration of resistive-less memcapacitor-based relaxation oscillators are proposed and closed form expressions for oscillation frequency and conditions for oscillation are derived in presence of nonlinear model. The proposed oscillator is verified using PSPICE simulation showing a perfect matching. [ABSTRACT FROM AUTHOR]

This paper presents the analysis for allocating the system poles and hence controlling the system stability for KHN and Sallen-Key fractional order filters. The stability analysis and stability contours for two different fractional order transfer functions with two different fractional order elements are presented. The effect of the transfer function parameters on the singularities of the system is demonstrated where the number of poles becomes dependent on the transfer function parameters as well as the fractional orders. Numerical, circuit simulation, and experimental work are used in the design to test the proposed stability contours. [ABSTRACT FROM AUTHOR]

Recently, there is an essential demand to extend the fundamentals of the conventional circuit theory to include the new generalized elements, fractional-order elements, and mem-elements due to their unique properties. This paper presents the relationships between seven different elements based on the four physical quantities and the fractional-order derivatives. One of them is the Fractional-order memristor, where the memristor dynamic is expressed by fractional-order derivative. This element merge the memristive and fractional-order concepts together where the conventional modeling becomes a special case. Moreover, the mathematical modeling of the fractional-order memristor is introduced. In addition, the response of applying DC, sinusoidal, and nonsinusoidal periodic signals is discussed. Finally, different numerical simulations are presented. [ABSTRACT FROM AUTHOR]

Recently, the mem-elements-based circuits have been addressed frequently in the nonlinear circuit theory due to their unique behavior. Thus, the modeling and characterizing of the mem-elements has become essential, especially studying their response under any excitation signal. This paper investigates the response of the meminductor under DC, sinusoidal, and periodic current signals for the first time. Furthermore, a meminductor emulator is developed to fit the obtained formulas which are built using commercial off the shelf components. The proposed analysis offers closed form expressions for the meminductance for each case. Moreover, many fundamentals and properties are derived to understand the responses such as the maximum saturation time in case of the DC response. A general closed form expression for the meminductance is derived under any periodic waveform, and this formula has been validated by applying a square wave as an example. [ABSTRACT FROM AUTHOR]

This paper introduces some generalized fundamentals for fractional-order RL C circuits as well as a gradient-based optimization technique in the frequency domain. One of the main advantages of the fractional-order design is that it increases the flexibility and degrees of freedom by means of the fractional parameters, which provide new fundamentals and can be used for better interpretation or best fit matching with experimental results. An analysis of the real and imaginary components, the magnitude and phase responses, and the sensitivity must be performed to obtain an optimal design. Also new fundamentals, which do not exist in conventional RLC circuits, are introduced. Using the gradient-based optimization technique with the extra degrees of freedom, several inverse problems in filter design are introduced. The concepts introduced in this paper have been verified by analytical, numerical, and PSpice simulations with different examples, showing a perfect matching. [ABSTRACT FROM AUTHOR]

This paper presents a general block diagram of a third-order linear differential equation using current mode techniques. The realization of the conjectured simplest chaotic equation of Elwakil and Kennedy based on Gm − C technology is given. The metal oxide semiconductor circuit is composed of 20 transistors and three grounded capacitors, can operate from a supply voltage as low as ±1.5 V, and covers a very wide range of frequencies. PSpice simulation results using 0.5 µm Mietec technology are given. A numerical solution is also included to verify the circuit operation. [ABSTRACT FROM AUTHOR]