Guest Editorial for the Special Issue on “Recent Advances in Simulation Methods, Modelling Approaches, and Physical Implementation of Fractional-Order Devices, Circuits, and Systems”

Abstract

Fractional calculus (FC) is currently associated with phenomena modeling that shows nonlocality and long memory effects in physics and engineering. In particular, the fractional-order operators provide an excellent approach to representing a physical phenomenon with improved accuracy because they capture the contributions from all past events contrary to classical calculus, whose nature is only local. For those reasons, the fractional order can be used as an extra degree of freedom to improve practical applications in various fields, such as analog and digital circuits, chaos theory, electronic devices, cryptography, control, signal processing, robotics, theory of filters, biology, wind turbines, viscoelastic studies, ferromagnetic materials, and so on. From a science and engineering point of view, there are still open problems in fractional calculus, ranging from numerical aspects and modeling techniques to the design and implementation of devices, circuits, and systems. For instance, optimized simulation methods are still needed to compute a proper solution considering the whole memory contributions of fractional operators but simultaneously reducing the computational effort. Classical fractional calculus definitions, as well as new operators (fractional-fractal, fractional operators in the complex plane, variable order calculus, etc.), should continue being explored to obtain novel models of physical phenomena at different levels of abstraction and descriptions, such as physical, circuit, macro, behavioral, and functional. In fractional-order devices, circuits, and systems, one of the challenges consists of implementing the fractional integrodifferential operator as integrators and derivators in the frequency domain, that is, $s^{\alpha }$ $\alpha \in R$ using approximation methods aiming for flexible and non-bulky realizations as there is no fabricated fractional-order capacitor yet commercially available.

The papers in this special issue are devoted to stimulating new ideas and methods and enabling the extension of numerous applications using fractional-order devices, circuits, and systems. High-quality contributions to numerical modeling, design, optimization, and implementation of devices and systems have been reported. In the paper “Fractional order capacitance behavior due to hysteresis effect of ferroelectric material on GaN HEMT devices [1],” Pyngrope et al. introduced a novel fractional-order capacitance model using the Grünwald–Letnikov derivative. The presented study is especially relevant to cope with the complex nature of the aluminum scandium nitride (AlScN) gate capacitance in GaN HEMTs (Gallium nitride (GaN))-High Electron Mobility Transistors, which have become the forefront of the semiconductor industry. The accuracy of the proposed model is demonstrated by numerous error metrics, gathering a robust mechanism for accurately characterizing GaN HEMT capacitance. In this manner, the proposed model represents a powerful approach to accurately describe the GaN HEMT capacitance as fractional order derivatives allow the modeling of noninteger order systems.

In the paper “Fractional-calculus analysis of the dynamics of typhoid fever with the effect of vaccination and carriers [2],” Jan et al. presented a novel epidemic model for typhoid fever with vaccination and carriers via Caputo-Fabrizio operator to minimize a global public health problem that affects considerable people annually. The findings highlighted the effectiveness of fractional order to describe the memory effects in the proposed model. In the paper “Design and performance analysis of 8-port multi-service quad-band MIMO antenna for automotive communication [3],” Arumugam et al. proposed a low-profile compact 8-port multiband antenna with polarization diversity principle for automotive communication. The presented design resonates at frequencies of 1.8, 2.4, 5.2, and 5.8 GHz for GSM, ISM bands, and WLAN wireless services tested on vehicular to intravehicular environments.

In the paper “Advanced tree-seed optimization based fractional-order PID controller design for simplified decoupled industrial tank systems [4],” Rajagopalan et al. analyzed the multiple issues of coupled tank systems by considering nonlinear dynamics, time delays, uncertainties, and cross-coupling effects. As a result, the study employed a fractional-order proportional–integral–derivative (FOPID) controller to regulate the level of a coupled tank system. In addition, the controller was optimized using a tree seed algorithm. Numerical experiments on distinct interconnected tank systems evidenced the efficiency of the fractional controller. In the paper “Exponential stability and numerical analysis of Timoshenko system with dual-phase-lag thermoelasticity [5],” Bouraoui et al. investigated the well-posedness and stability of a thermoelastic Timoshenko system with non-Fourier heat conduction. In particular, a dual-phase-lag (DPL) model with two thermal relaxation times was considered. The semigroup approach and Gearhart–Prüss theorem were valuable tools to demonstrate the existence, uniqueness, and exponential stability, respectively. Finally, in the paper “Comparative analysis of uncontrollable angles in direct torque and stator flux control and rotor flux control strategies: A numerical and experimental study [6],” Alshbib et al. reported an analysis of uncontrollable angles (UAs) in the direct torque control (DTC) algorithm at different operating conditions, including parameter variations in two distinct strategies: Direct torque and stator flux control (DTC-SC) and (DTC-RC). Using data from wide speed, stator and rotor variations, and load changes, the proposed control can be practical to diverse operation modes such as variable speed, variable stator and rotor resistance, and variable load. Experimental tests on a DS1103 platform verified the theoretical analysis.

The Guest Editors are excited to present this special issue. We expect our collected works to inspire researchers to strive for further advances in the emerging fields of devices, circuits, and systems and their applications under fractional-order calculus. The Guest Editors would like to thank the authors of all the high-quality papers submitted on this research topic. We would also like to thank Prof. Giovanni Crupi (Editor-in-Chief of Int J Numer Model) for facilitating this special issue and the reviewers and the Journal's Editorial Board for being very encouraging and supportive. We hope you enjoy reading this special issue in this exciting and fast-evolving field as much as we have done!

The authors declare no conflicts of interest.