This paper is dedicated to develop a fractional order model of the rate of change of cancerous blood cells in Chronic Myeloid Leukaemia using fractional-order differential equations as well as tackling the factors that affect this rate and compare between them
Generalization of third-order low pass filters to the fractional-order domain with experimental results
This paper is concerned with the generalization of continuous-time 3rd order low-pass filters to the fractional order domain
Parameter Identification of Flexible Supercapacitors with Fractional Cuckoo Search
In this paper, we identify the model parameters of flexible supercapacitors from time-domain data using fractional cuckoo search
A fractional-order dynamic PV model
A dynamic model of Photo-Voltaic (PV) solar module is important when it is utilized in conjunction with switching circuits and in grid connected applications
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.
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.
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.
Applications of continuous-time fractional order chaotic systems
The study of nonlinear systems and chaos is of great importance to science and engineering mainly because real systems are inherently nonlinear and linearization is only valid near the operating point. The interest in chaos was increased when Lorenz accidentally discovered the sensitivity to initial condition during his simulation work on weather prediction. When a nonlinear system is exhibiting deterministic chaos, it is very difficult to predict its response under external disturbances. This behavior is a double-edged weapon. From a control and synchronization point of view, this proposes a challenge. On the other hand, from a communications and encryption perspective, this provides a higher level of security. This chapter is a survey of the recent contributions in engineering applications of fractional order chaotic continuous-time systems. The applications include but not limited to: communication and encryption, FPGA implementations, synchronization and control, modeling of electric motors, and biomedical applications. © 2018 Elsevier Inc. All rights reserved.
Discrete fractional-order Caputo method to overcome trapping in local optima: Manta Ray Foraging Optimizer as a case study
Enhancing the exploration and exploitation phases of the metaheuristic (MH) optimization algorithms is the key to avoiding local optima. The Manta ray foraging optimizer is a recently proposed MH optimizer. The MRFO showed a good performance in the simple optimization problems. However, it is trapped into the local optimum in the more elaborated ones due to the original algorithm’s low capability in exploiting the optimal solutions and its convergence. From this principle, in this work, a novel variant of the Manta ray foraging optimizer has been proposed for global optimization problems, engineering design optimization problems, and multi-threshold segmentation. In the proposed approach, the fractional calculus (FC) using Caputo fractional differ-sum operator has been adopted to enhance the manta rays movement in the exploitation phase via utilizing history dependency of FC to boost exploiting the optimal solutions via sharing the past knowledge over the optimization process. Moreover, to avoid premature convergence, the somersault factor has been adaptively tuned. The fractional-order Caputo Manta-Ray Foraging Optimizer (FCMRFO) has been proposed. The proposed algorithm’s sensitivity for the FC coefficients has been tested with ten-dimensional CEC2017 benchmarks. The scalability test of the proposed algorithm has been performed with 30, 50 and 100-dimensional CEC2017. Moreover, CEC2020 benchmarks with dimensions 5 and 20 have been applied for providing an extensive investigation, and the FCMRFO has been compared with recent state-of-the-art algorithms. Through utilizing the non-parametric statistical analysis and ranking test, the FCMRFO confirms its superiority and ability to avoid the local optimum in several cases. For the second part of the study, three constrained engineering design problems have been investigated; then, numerous natural images are applied to appraise the FCMRFO for multilevel threshold image segmentation. By performing several metrics, the FCMRFO proves its quality and efficiency compared to recent well-regarded algorithms in engineering applications and image segmentation. © 2021
Fractional order Chebyshev-like low-pass filters based on integer order poles
Chebyshev filter is one of the most commonly used prototype filters that approximate the ideal magnitude response. In this paper, a simple and fast approach to create fractional order Chebyshev-like filter using its integer order poles is discussed. The transfer functions for the fractional filters are developed using the integer order poles from the traditional filter. This approach makes this work the first to generate fractional order transfer functions knowing their poles. The magnitude, phase, step responses, and group delay are simulated for different fractional orders showing their Chebyshev-like characteristics while achieving a fractional order slope. Circuit simulations using Advanced Design Systems of active and passive realizations of the proposed filters are also included and compared with Matlab numerical simulations proving the reliability of the design procedure. Experimental results of a two-stage active realization show good accordance with ADS and Matlab results. © 2019 Elsevier Ltd