Special Issue "Fractional-Order Circuit Theory and Applications"

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: closed (31 January 2022) | Viewed by 3179

Special Issue Editors

Prof. Dr. Costas Psychalinos
E-Mail Website1 Website2
Guest Editor
Department of Physics, Electronics Laboratory, University of Patras, 26504 Patras, Greece
Interests: fractional-order circuits and systems; analog integrated circuits; fractional-order biomedical circuits; fractional-order filters
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Ahmed Radwan
E-Mail Website
Guest Editor
Vice President for Research, School of Engineering and Applied Sciences, Nile University, Sheikh Zayed City 12588, Egypt
Interests: fractional-order circuits and systems; chaotic systems; oscillators; filters; encryption; bioimpedance; modeling; numerical analysis
Prof. Dr. Blas M. Vinagre
E-Mail Website
Guest Editor
Industrial Engineering School, University of Extremadura, Av. Elvas s/n, 06006 Badajoz, Spain
Interests: fractional calculus; control theory and applications; mobile and flexible robotics; microrobotics
Special Issues, Collections and Topics in MDPI journals
Dr. Karabi Biswas
E-Mail Website
Guest Editor
Department of Electrical Engineering, Indian Institute of Technology Kharagpur, West Bengal 721302, India
Interests: fractional order device fabrication; fractional order circuit design; sensors and instrumentation system design

Special Issue Information

Dear Colleagues,

One of the advantages of fractional-order calculus is that it permits more accurate mathematical modelling than its integer-order counterpart, especially in real-life application. This is due to the extra degrees of freedom attained by introducing fractional orders as new parameters.

The rapid growth of fractional calculus applications in science and engineering has also motivated new formulations and mathematical definitions, especially in the circuits and systems, such as filters, encryption, bio-engineering, control systems, robotics, chaotic systems, oscillators, wireless power transmission, and super-capacitor modeling.

The focus of this Special Issue is on the recent advances of these applications. The topics of interest include (but are not limited to):

  • Analog and digital realization of fractional-order operators
  • Approximations of the fractional-order derivatives and their applications in circuit design
  • Circuit implementation, analysis, and fabrication of fractional-order components
  • Fractional calculus models in physics, electrochemistry, and fluid mechanics
  • Fractional-order control and its applications
  • Fractional-order chaotic systems and their implementation
  • Fractional-order bioimpedance models and biomedical circuits
  • Fractional-order mem-elements, modeling and applications
  • Fractional-order models for energy storage devices and systems
  • Fractional-order circuits for machine learning
  • Fractional-order nonlinear circuits and systems

This Special Issue is in cooperation with the NILES Conference 2021 (https://www.nilesconf.org) and welcomes submissions from participants of the conference.

Prof. Dr. Costas Psychalinos
Prof. Dr. Ahmed Radwan
Prof. Dr. Blas Vinagre
Dr. Karabi Biswas
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fractional-order circuits
  • fractional-order components
  • approximation techniques
  • fractional-order models
  • fractional-order bioimpedance
  • fractional-order chaotic systems
  • fractional-order mem-elements
  • energy storage devices
  • machine learning

Published Papers (3 papers)

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Research

Article
Rational Approximations of Arbitrary Order: A Survey
Fractal Fract. 2021, 5(4), 267; https://doi.org/10.3390/fractalfract5040267 - 08 Dec 2021
Cited by 2 | Viewed by 811
Abstract
This paper deals with the study and analysis of several rational approximations to approach the behavior of arbitrary-order differentiators and integrators in the frequency domain. From the Riemann–Liouville, Grünwald–Letnikov and Caputo basic definitions of arbitrary-order calculus until the reviewed approximation methods, each of [...] Read more.
This paper deals with the study and analysis of several rational approximations to approach the behavior of arbitrary-order differentiators and integrators in the frequency domain. From the Riemann–Liouville, Grünwald–Letnikov and Caputo basic definitions of arbitrary-order calculus until the reviewed approximation methods, each of them is coded in a Maple 18 environment and their behaviors are compared. For each approximation method, an application example is explained in detail. The advantages and disadvantages of each approximation method are discussed. Afterwards, two model order reduction methods are applied to each rational approximation and assist a posteriori during the synthesis process using analog electronic design or reconfigurable hardware. Examples for each reduction method are discussed, showing the drawbacks and benefits. To wrap up, this survey is very useful for beginners to get started quickly and learn arbitrary-order calculus and then to select and tune the best approximation method for a specific application in the frequency domain. Once the approximation method is selected and the rational transfer function is generated, the order can be reduced by applying a model order reduction method, with the target of facilitating the electronic synthesis. Full article
(This article belongs to the Special Issue Fractional-Order Circuit Theory and Applications)
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Article
FPAA-Based Realization of Filters with Fractional Laplace Operators of Different Orders
Fractal Fract. 2021, 5(4), 218; https://doi.org/10.3390/fractalfract5040218 - 13 Nov 2021
Cited by 1 | Viewed by 368
Abstract
A simple and direct procedure for implementing fractional-order filters with transfer functions that contain Laplace operators of different fractional orders is presented in this work. Based on a general fractional-order transfer function that describes fractional-order low-pass, high-pass, band-pass, band-stop and all-pass filters, the [...] Read more.
A simple and direct procedure for implementing fractional-order filters with transfer functions that contain Laplace operators of different fractional orders is presented in this work. Based on a general fractional-order transfer function that describes fractional-order low-pass, high-pass, band-pass, band-stop and all-pass filters, the introduced concept deals with the consideration of this function as a whole, with its approximation being performed using a curve-fitting-based technique. Compared to the conventional procedure, where each fractional-order Laplace operator of the transfer function is individually approximated, the main offered benefit is the significant reduction in the order of the resulting rational function. Experimental results, obtained using a field-programmable analog array device, verify the validity of this concept. Full article
(This article belongs to the Special Issue Fractional-Order Circuit Theory and Applications)
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Article
CMOS OTA-Based Filters for Designing Fractional-Order Chaotic Oscillators
Fractal Fract. 2021, 5(3), 122; https://doi.org/10.3390/fractalfract5030122 - 14 Sep 2021
Cited by 3 | Viewed by 962
Abstract
Fractional-order chaotic oscillators (FOCOs) have shown more complexity than integer-order chaotic ones. However, the majority of electronic implementations were performed using embedded systems; compared to analog implementations, they require huge hardware resources to approximate the solution of the fractional-order derivatives. In this manner, [...] Read more.
Fractional-order chaotic oscillators (FOCOs) have shown more complexity than integer-order chaotic ones. However, the majority of electronic implementations were performed using embedded systems; compared to analog implementations, they require huge hardware resources to approximate the solution of the fractional-order derivatives. In this manner, we propose the design of FOCOs using fractional-order integrators based on operational transconductance amplifiers (OTAs). The case study shows the implementation of FOCOs by cascading first-order OTA-based filters designed with complementary metal-oxide-semiconductor (CMOS) technology. The OTAs have programmable transconductance, and the robustness of the fractional-order integrator is verified by performing process, voltage and temperature variations as well as Monte Carlo analyses for a CMOS technology of 180 nm from the United Microelectronics Corporation. Finally, it is highlighted that post-layout simulations are in good agreement with the simulations of the mathematical model of the FOCO. Full article
(This article belongs to the Special Issue Fractional-Order Circuit Theory and Applications)
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