The efficiency of the hardware implementations of fractional-order systems heavily relies on the efficiency of realizing the fractional-order derivative operator. In this work, a generic hardware implementation of the fractional-order derivative based on the Grünwald–Letnikov’s approximation is proposed and verified on a field-programmable gate array. The main advantage of this particular realization is its flexibility in applications which enable easy real-time configuration of the values of the fractional orders, step sizes, and/or other system parameters without changing the hardware

In this work, we demonstrate the possibility of performing two-dimensional rotation on a chaotic system. This enables the rotation of its attractor in space without changing its chaotic dynamics. In particular, the rotated system preserves the same eigenvalues at all equilibrium points and its largest Lyapunov exponent remains unchanged. Two chaotic systems, one of which is the classical Lorenz system, are used to illustrate and validate the rotation operation using numerical simulations and further experimentally using a digital FPGA platform. © 2019, Springer Science+Business Media, LLC

Chaos is described as a unstable dynamic behavior with dependence on initial conditions. The control and synchronization of chaotic systems requires the knowledge of parameters in advance. Recently researcher's has been shifted from integer order chaotic system to fraction order chaotic system. In this work, based on the stability theory of integer-order linear systems and Lyapunov stability theory, we present some control schemes to achieve a new type of synchronization called inverse generalized synchronization between different dimensional integer and fractional-orders chaotic systems. The

Due to the non-idealities of commercial inductors, the demand for a better model that accurately describe their dynamic response is elevated. So, the fractional order models of Buck, Boost and Buck-Boost DC-DC converters are presented in this paper. The detailed analysis is made for the two most common modes of converter operation: Continuous Conduction Mode (CCM) and Discontinuous Conduction Mode (DCM). Closed form time domain expressions are derived for inductor currents, voltage gain, average current, conduction time and power efficiency where the effect of the fractional order inductor is

The Cole–Davidson function is an efficient tool for describing the tissue behavior, but the conventional methods of approximation are not applicable due the form of this function. In order to overcome this problem, a novel scheme for approximating the Cole–Davidson function, based on the utilization of a curve fitting procedure offered by the MATLAB software, is introduced in this work. The derived rational transfer function is implemented using the conventional Cauer and Foster RC networks. As an application example, the impedance model of the membrane of mesophyll cells is realized, with

Characterizing and modeling electrical energy storage devices is essential for their proper integration in larger systems. However, basic circuit elements, i.e. resistors, inductors, and capacitors, are not well-suited to explain their complex frequency-dependent behaviors. Instead, fractional-order models, which are based on non-integer-order differential equations in the time-domain and include for instance the constant phase element (CPE), are mathematically more fit to this end. Here, the electrical power and energy of fractional-order capacitance and inductance are derived in both steady

This paper presents a semi-analytical method for solving fractional differential equations with strong terms like (exp, sin, cos,…). An auxiliary parameter is introduced into the well-known Picard's method and so called controlled Picard's method. The proposed approach is based on a combination of controlled Picard's method with Simpson rule. This approach can cover a wider range of integer and fractional orders differential equations due to the extra auxiliary parameter which enhances the convergence and is suitable for higher order differential equations. The proposed approach can be

This paper introduces an FPGA design methodology of a sample and bit permutation speech encryption system. Pipelining method is used to build the proposed system, which can have different number of permutation levels. The security of the system is evaluated using entropy, Mean Squared Error (MSE) and correlation coefficients comparing the different permutation levels. The results demonstrate the security of the proposed system, which enables its utilization in speech telecommunication. Hardware resources comparison validates the efficiency of the system. The designs are simulated using Xilinx

The fractional-order lung impedance model of the human respiratory tree is implemented in this paper, using Operational Transconductance Amplifiers. The employment of such active element offers electronic adjustment of the impedance characteristics in terms of both elements values and orders. As the MOS transistors in OTAs are biased in the weak inversion region, the power dissipation and the dc bias voltage of operation are also minimized. In addition, the partial fraction expansion tool has been utilized, in order to achieve reduction of the spread of the required time-constants and scaling

Double-exponent fractional-order impedance functions are important for modeling a wide range of biochemical materials and biological tissues. Through appropriate selection of the two exponents (fractional orders), the well-known Havriliak–Negami, Cole–Cole, Cole–Davidson, and Debye relaxation models can be obtained as special cases. Here we show that an integer-order Padé-based approximation of the Havriliak–Negami function is possible to obtain and can be realized using appropriately configured Cauer/Foster resistor-capacitor (RC) networks. Two application examples are subsequently examined