One of the advantages of fractional order is the extra degree of freedom added by the fractional-order parameters, which enrich the analysis with more details in new dimensions. This chapter introduces factional-order conventional filters of orders ?, 2?, and 3?. The general transfer functions of continuous-time filters (low-pass, high-pass, and band-pass filters) to the noninteger-order (fractional-order) domain are investigated. Also, mathematical expressions for the maximum and minimum frequencies, the half power frequencies, and the right-phase frequencies are derived. In addition, the effect of the transfer function parameters on the filter poles and hence the stability is introduced. Numerical spice results are introduced to validate the theoretical findings. Several passive and active filters are studied to validate the concept. This chapter also investigates the effect of an inserted delay parameter on the filter main frequencies. Different filter responses are obtained from the general delayed transfer function. Two delay examples are investigated. © 2018 Elsevier Inc. All rights reserved.
FPGA Implementation of Fractional-Order Chaotic Systems
This chapter introduces two FPGA implementations of the fractional-order operators: the Caputo and the Grünwald-Letnikov (GL) derivatives. First, the Caputo derivative is realized using nonuniform segmentation to reduce the size of the Look-Up Table. The Caputo implementation introduced can generate derivatives of previously defined functions only. Generic and complete hardware architecture of the GL operator is realized with different memory window sizes. The generic architecture is used as a block to implement several fractional-order chaotic systems. The investigated systems include Borah, Chen, Liu, Li, and Arneodo fractional-order chaotic systems. Different interesting attractors are realized under various parametric changes with distinct step sizes for different fractional orders. To verify the chaotic behavior of the generated attractors, the Maximum Lyapunov Exponent is calculated for each system at different parameter values. © 2018 Elsevier Inc. All rights reserved.
Survey on Two-Port Network-Based Fractional-Order Oscillators
This chapter merges the fractional calculus and two-port networks in oscillator design. The fractional-order elements ? and ? add extra degrees of freedom that increase the design flexibility and frequency band while providing control over the phase difference. A prototype of the fractional-order two-port network oscillators is introduced. It consists of a general two-port network and three impedances distributed as input, output, and a feedback impedance. Three different two-port network classifications are obtained according to the ground location. This chapter focuses on one of these classifications from which two derived prototypes can be extracted. The general analytical formulas of the oscillation frequency and condition as well as the phase difference are derived in terms of the transmission matrix parameter of a general two-port network. Different active building blocks are used to serve as a two-port network. Numerical, Spice simulations, and experimental results are given to validate the presented analysis. © 2018 Elsevier Inc. All rights reserved.
On the Approximation of Fractional-Order Circuit Design
Despite the complex nature of fractional calculus, it is still fairly possible to reduce this complexity by using integer-order approximation. Each integer-order approximation has its own trade-offs from the complexity, sensitivity, and accuracy points of view. In this chapter, two different fractional-order electronic circuits are studied: the Wien oscillator and the CCII-based KHN filter with two different fractional elements of orders ? and ?. The investigation is concerned with changes in the response of these two circuits under two approximations: Oustaloup and Matsuda. A detailed review of each approximation technique is provided as well as its design procedure. Oscillator and filter responses are simulated using MATLAB. Foster-I realization is used to implement the approximated Wien oscillator and filter transfer functions as circuits in order to simulate them in PSpice. The responses are compared to the exact solution to investigate which achieves the lowest error. For oscillators, the comparison is based on oscillation condition and oscillation frequency while for filters, the focus is on filter fundamental frequencies. This is a big issue in filter design: maximum or minimum frequency, right phase frequency, and half-power frequency. © 2018 Elsevier Inc. All rights reserved.
Fractional-order oscillators based on a single Op-Amp
This chapter introduces a family of fractional-order oscillators based on a single operational amplifier (Op-Amp) with two fractional-order capacitors. Twelve different fractional-order oscillator circuits are investigated where the state matrix, oscillation frequency, and oscillation condition for each circuit are presented. The phase difference between the two oscillatory outputs is deduced in terms of the fractional-order parameters. The fractional-order parameter enhances the oscillator performance by providing an extra degree-of-freedom. Also, the resulting circuits provide independent controllability for the phase difference and the oscillation frequency. Numerical simulations using MATLAB® are performed to study the effect of the fractional-order parameters on the circuit response. Moreover, PSpice simulations are performed on different cases using two different fractional-order capacitors. Selected cases are verified experimentally to confirm the theoretical findings. © 2022 Elsevier Inc. All rights reserved.
Biologically Inspired Optimization Algorithms for Fractional-Order Bioimpedance Models Parameters Extraction
This chapter introduces optimization algorithms for parameter extractions of three fractional-order circuits that model bioimpedance. The Cole-impedance model is investigated; it is considered one of the most commonly used models providing the best fit with the measured data. Two new models are introduced: the fractional Hayden model and the fractional-order double-shell model. Both models are the generalization of their integer-order counterpart. These fractional-order models provide an improved description of observed bioimpedance behavior. New metaheuristic optimization algorithms for extracting the impedance parameters of these models are investigated. The proposed algorithms inspired by nature are known as the Flower Pollination Algorithm, the Grey Wolf Optimizer, the Moth-flame Optimizer, the Whale Optimization Algorithm, and the Grasshopper Optimization Algorithm. These algorithms are tested over sets of simulated and experimental data. Their results are compared with a conventional fitting algorithm (the nonlinear least square) in aspects of speed, accuracy, and precision. © 2018 Elsevier Inc. All rights reserved.
Modeling woody plant tissue using different fractional-order circuits
This chapter presents results on the most suitable bio-impedance circuits for modeling woody plants. The modified double-shell, the modified triple Cole-Cole, and the traditional wood circuit models are compared for fitting experimentally measured data. Consequently, a modified circuit model is proposed. This model gives the best results for all interelectrode spacing distances when compared to the other circuits. All impedance data have been measured using the research-grade SP150 electrochemical station in the frequency range 0.1 Hz to 200 kHz. The fitting is done using the Zfit of the impedance analyzer SP150. © 2022 Elsevier Inc. All rights reserved.
Carbon Nanomaterials and Their Composites as Adsorbents
Carbon nanomaterials with various nanostructures (carbon nanotubes, graphene, graphene oxide, fullerene, nano diamonds, carbon quantum dots, carbon nanofibers, graphitic carbon nitrides, and nano porous carbons) are the decade’s most distinguishing and popular materials. They have distinctive physicochemical qualities such as chemical stability, mechanical strength, hardness, thermal and electrical conductivities, and so on. Furthermore, they are easily surface functionalized and tweaked, modifying them for high-end specific applications. Carbon nanostructures’ properties and surface characteristics are determined by the synthesis method used to create them. Nanoscience and nanotechnology have the potential to create materials with unexpected functions and qualities, which are transforming all industries. Carbon nanoparticles such as fullerene, carbon nanotubes, and graphene stand out among the various kinds of nanomaterials. These nanoparticles offer a wide range of practical applications, particularly in adsorption processes. Carbon nanoparticles exhibit unique structures that could be used in the construction of extremely sensitive, selective, and effective adsorbent devices for the removal of inorganic, organic, and biological pollutants from water solutions, as well as nano sensors and drug delivery systems. In this chapter, we demonstrated the number of studies published in recent years that used carbon nanomaterials as adsorbents. Furthermore, this chapter discusses essential features of adsorption and different nanocarbon carbon composite material, such as the contrast between physical and chemical absorption. Furthermore, diverse carbon nanomaterial synthesis such as AC–FeO ?Cu and Bimetallic FeO ?Cu/algae activated carbon composites AC–Fe0 ?Cu methodologies, functionalization, and characteristics are provided and logically addressed. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.
Memcapacitor based applications
This chapter is divided into three sections focusing on some memcapacitor-based applications. The first one discusses the mathematical analyses and design of resistive-less memcapacitor-based relaxation oscillators where different cases have been investigated and validated. Analytical expressions for the oscillation frequency, duty cycle, stored energy, and conditions of oscillation have been achieved with many numerical examples and circuit simulations. The second section discusses the boundary effect on the analysis and output behavior of memcapacitor-based oscillators compared to the previous case. The last section addresses the memcapacitor-bridge synapses with mathematical analysis, weight programming, and circuit simulations. © 2015, Springer International Publishing Switzerland.
Memristor-based multilevel digital systems
This chapter investigates the advantages of memristor-based digital applications using multi-level arithmetic concepts. Recently, there are huge concerns regarding the memristor in digital signal processing (DSP) circuits to enhance the performance and realize very high density, nonvolatile memories in neural networks. This can be achieved by mapping the high/low logic into the memristor high/low resistances. Recently, the potential to divide the memristance levels to build multilevel digital circuits such as the ternary and redundant circuits are discussed. The concepts have been initiated by designing a half ternary adder based on the memristor; then, the concept is generalized for redundant half adder, full adder, and N-bit adder circuits. The advantages of such circuits that the speed is independent on the operand and parallel processing can be handled efficiently. Moreover, a general approach to build digital functions using mixed memristor-transistor circuits are investigated such as multipliers. © 2015, Springer International Publishing Switzerland.