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Fractal Fract
Special Issues
Fractional-Order Circuits, Systems, and Signal Processing, 2nd Edition
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Fractional-Order Circuits, Systems, and Signal Processing, 2nd Edition

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

Deadline for manuscript submissions: 25 December 2024 | Viewed by 4666

Special Issue Editors

Dr. Norbert Herencsar

E-Mail Website
Guest Editor
Department of Telecommunications, Brno University of Technology, 61600 Brno, Czech Republic
Interests: energy storage elements; fractional-order circuits and systems; impedance spectroscopy; nano/microelectronics; nanodevices; organic electronics and tissue engineering; sensory processing circuits and systems; supercapacitors
Special Issues, Collections and Topics in MDPI journals
Dr. Shibendu Mahata

E-Mail Website
Guest Editor
Department of Electrical Engineering, Dr. B. C. Roy Engineering College, Durgapur 713206, West Bengal, India
Interests: analog electronics; signal processing; optimization; fractional-order filter; control theory
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Esteban Tlelo-Cuautle

E-Mail Website
Guest Editor
Department of Electronics, Instituto Nacional de Astrofísica, Optica y Electrónica (INAOE), Tonantinztla, Puebla 72840, Mexico
Interests: analog signal processing; integrated circuits; optimization by meta-heuristics; fractional-order chaotic systems; security in internet of things; analog/RF and mixed-signal design automation tools
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Ivo Petráš

E-Mail Website
Guest Editor
Faculty of Mining, Ecology, Process Control and Geotechnologies (FBERG), Technical University of Kosice (TUKE), Kosice, Slovakia
Interests: fractional calculus and its applications; dynamical systems; chaos theory; control theory; mathematical modelling; simulations; process control; automation; signal processing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fractional calculus is the branch of mathematics that generalizes the operations of classical calculus. The dynamics of real-world systems can be more effectively captured using the concepts of fractional calculus compared to classical calculus-based models. This is due to the additional degrees-of-freedom (extra ‘tuning knobs’) available in a fractional-order transfer function, which, in turn, enhances the design flexibility. The application of numerical approximation methods has resulted in effective fractional-order systems for various engineering disciplines, such as linear and non-linear circuit theory, signal processing, biomedicine, control theory, etc. In recent years, optimization (both classical and metaheuristic) techniques have also been exploited by researchers to obtain robust fractional-order models.

The focus of this Special Issue is to further advance the theory, design, realization, and application domain of fractional-order systems.

The first volume of this Special Issue was a great success with 15 papers published, which can be read at: Fractal Fract | Special Issue : Fractional-Order Circuits, Systems, and Signal Processing (mdpi.com)

Dr. Norbert Herencsar
Dr. Shibendu Mahata
Prof. Dr. Esteban Tlelo-Cuautle
Prof. Dr. Ivo Petráš
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 2700 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 analog filters, oscillators, PLLs
  • fractional-order filters for digital signal and image processing
  • fractional-order neural networks for signal processing
  • modeling of fractance behavior using active/passive elements
  • fabrication of fractance elements
  • fractional-order modeling of batteries
  • fractional-order control systems
  • fractional-order bioimpedance modeling

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (4 papers)

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Research

20 pages, 3351 KiB  
Article
A Delayed Fractional-Order Predator–Prey Model with Three-Stage Structure and Cannibalism for Prey
by Hui Zhang and Ahmadjan Muhammadhaji
Fractal Fract. 2024, 8(8), 492; https://doi.org/10.3390/fractalfract8080492 - 21 Aug 2024
Viewed by 507
Abstract
In this study, we investigate a delayed fractional-order predator–prey model with a stage structure and cannibalism. The model is characterized by a three-stage structure of the prey population and incorporates cannibalistic interactions. Our main objective is to analyze the existence, uniqueness, boundedness, and [...] Read more.
In this study, we investigate a delayed fractional-order predator–prey model with a stage structure and cannibalism. The model is characterized by a three-stage structure of the prey population and incorporates cannibalistic interactions. Our main objective is to analyze the existence, uniqueness, boundedness, and local stability of the equilibrium points of the proposed system. In addition, we investigate the Hopf bifurcation of the system, taking the digestion delay of the predator as the branch parameter, and clarify the necessary conditions for the existence of the Hopf bifurcation. To confirm our theoretical analysis, we provide a numerical example to validate the accuracy of our research results. In the conclusion section, we carefully review the results of the numerical simulation and propose directions for future research. Full article
(This article belongs to the Special Issue Fractional-Order Circuits, Systems, and Signal Processing, 2nd Edition)
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21 pages, 7253 KiB  
Article
Modeling and Control Research of Fractional-Order Cascaded H-Bridge Multilevel STATCOM
by Junhua Xu, Songqin Tang, Guopeng He, Zheng Gong, Guangqing Lin and Jiayu Liu
Fractal Fract. 2024, 8(7), 392; https://doi.org/10.3390/fractalfract8070392 - 29 Jun 2024
Cited by 1 | Viewed by 643
Abstract
This paper introduces fractional-order capacitors and fractional-order inductors into the conventional integer-order cascaded H-bridge multilevel static compensator (ICHM-STATCOM), thereby constructing the main circuit of the fractional-order cascaded H-bridge multilevel static compensator (FCHM-STATCOM). Mechanism-based modeling is employed to establish switching function models and low-frequency [...] Read more.
This paper introduces fractional-order capacitors and fractional-order inductors into the conventional integer-order cascaded H-bridge multilevel static compensator (ICHM-STATCOM), thereby constructing the main circuit of the fractional-order cascaded H-bridge multilevel static compensator (FCHM-STATCOM). Mechanism-based modeling is employed to establish switching function models and low-frequency dynamic models for the FCHM-STATCOM in the three-phase stationary coordinate system (a-b-c). Subsequently, fractional-order rotating coordinate transformation is introduced to establish the mathematical model of the FCHM-STATCOM in the synchronous rotating coordinate system (d-q). Additionally, a fractional-order proportional-integral (FOPI)-based fractional-order dual closed-loop current decoupling control strategy is proposed. Finally, this paper validates the correctness of the established mathematical models through digital simulation. Moreover, the simulation results demonstrate that by appropriately selecting the order of fractional-order capacitors and fractional-order inductors, the FCHM-STATCOM exhibits superior dynamic and static characteristics compared to the conventional ICHM-STATCOM, and the FCHM-STATCOM provides a more flexible reactive power compensation solution for power systems. Full article
(This article belongs to the Special Issue Fractional-Order Circuits, Systems, and Signal Processing, 2nd Edition)
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16 pages, 4092 KiB  
Article
Dynamic Analysis and Sliding Mode Synchronization Control of Chaotic Systems with Conditional Symmetric Fractional-Order Memristors
by Huaigu Tian, Mingwei Zhao, Jindong Liu, Qiao Wang, Xiong Yu and Zhen Wang
Fractal Fract. 2024, 8(6), 307; https://doi.org/10.3390/fractalfract8060307 - 23 May 2024
Cited by 17 | Viewed by 1062
Abstract
In this paper, the characteristics of absolute value memristors are verified through the circuit implementation and construction of a chaotic system with a conditional symmetric fractional-order memristor. The dynamic behavior of fractional-order memristor systems is explored using fractional-order calculus theory and the Adomian [...] Read more.
In this paper, the characteristics of absolute value memristors are verified through the circuit implementation and construction of a chaotic system with a conditional symmetric fractional-order memristor. The dynamic behavior of fractional-order memristor systems is explored using fractional-order calculus theory and the Adomian Decomposition Method (ADM). Concurrently, the investigation probes into the existence of coexisting symmetric attractors, multiple coexisting bifurcation diagrams, and Lyapunov exponent spectra (LEs) utilizing system parameters as variables. Additionally, the system demonstrates an intriguing phenomenon known as offset boosting, where the embedding of an offset can adjust the position and size of the system’s attractors. To ensure the practical applicability of these findings, a fractional-order sliding mode synchronization control scheme, inspired by integer-order sliding mode theory, is designed. The rationality and feasibility of this scheme are validated through a theoretical analysis and numerical simulation. Full article
(This article belongs to the Special Issue Fractional-Order Circuits, Systems, and Signal Processing, 2nd Edition)
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11 pages, 7253 KiB  
Article
Novel Low-Pass Two-Dimensional Mittag–Leffler Filter and Its Application in Image Processing
by Ivo Petráš
Fractal Fract. 2023, 7(12), 881; https://doi.org/10.3390/fractalfract7120881 - 13 Dec 2023
Cited by 4 | Viewed by 1654
Abstract
This paper presents an innovative Mittag–Leffler two-dimensional filter and its application in image processing. The proposed filter leverages the utilization of a Mittag–Leffler function within the probability density function. It introduces three adjustable filter parameters that enable the manipulation of the curve shape [...] Read more.
This paper presents an innovative Mittag–Leffler two-dimensional filter and its application in image processing. The proposed filter leverages the utilization of a Mittag–Leffler function within the probability density function. It introduces three adjustable filter parameters that enable the manipulation of the curve shape and the filter’s forgetting factor. Moreover, a two-dimensional Mittag–Leffler distribution was defined and used for the first time in an image filter. By conducting a comparative analysis against conventional filtering techniques, the paper showcases the distinct advantages of the proposed filter through illustrative examples. Additionally, the paper provides detailed implementation explanations and presents the Matlab function corresponding to the proposed two-dimensional filter. Full article
(This article belongs to the Special Issue Fractional-Order Circuits, Systems, and Signal Processing, 2nd Edition)
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