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Fractal Fract
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Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement...
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Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing​ Algorithms, Second Edition

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

Deadline for manuscript submissions: closed (25 August 2025) | Viewed by 2830

Special Issue Editors

Dr. Jin-Xi Zhang

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Guest Editor
State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China
Interests: fractional-order systems; nonlinear systems; multi-agent systems; prescribed performance control; nonlinear control
Special Issues, Collections and Topics in MDPI journals
Dr. Xuefeng Zhang

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Guest Editor
College of Sciences, Northeastern University, Shenyang 110819, China
Interests: singular systems; fractional systems; robust control
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Driss Boutat

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Guest Editor
Institut National des Sciences Appliquées Centre Val de Loire, Bourges, France
Interests: non-asymptotic state estimation; non-asymptotic fractional order differentiator
Special Issues, Collections and Topics in MDPI journals
Dr. Da-Yan Liu

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Guest Editor
INSA Centre Val de Loire, Université d’Orléans, PRISME EA 4229, CEDEX, 18022 Bourges, France
Interests: estimation and control for fractional order systems; numerical solutions for fractional order differential equations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent years, a growing number of studies from various science and engineering fields have dealt with dynamical systems described by the connection between the theory of artificial intelligence and fractional differential equations, with many computational fractional intelligence systems and their stability analysis and image processing applications having been proposed. The aim of this Special Issue is to gather articles reflecting the latest developments in applied mathematics and advanced intelligent control engineering related to the interdisciplinary topics of control, fractional calculus, and image processing, and their applications in engineering science. Fractional calculus and fractional processes, with applications in control systems and image processing, have become a topic of interest. Fractional-order systems are a natural generalization of classical integer-order systems and can accurately describe many real-world physical systems. Fusion and noise suppression of medical images are becoming increasingly difficult to ignore in image processing, and these techniques provide abundant information for clinical diagnosis and treatment. Image fusion is a significant factor in image processing, owing to the increase in image acquisition models. Recently, fractional operators have been playing an important role in image processing. Additionally, powerful fractional operating tools have been introduced that can be effectively applied to the analysis and design of nonlinear control systems. Singular systems are governed by so-called singular differential equations, which endow the systems with many special features that are not found in classical systems. The approaches of fractional-order control systems, which borrow from those of integer-order control systems, are attracting increasing attention within the control field.

Please feel free to explore our previous editions:

https://www.mdpi.com/journal/fractalfract/special_issues/fractional_image_control and https://www.mdpi.com/journal/fractalfract/special_issues/fractional_image2.

Dr. Jin-Xi Zhang
Dr. Xuefeng Zhang
Prof. Dr. Driss Boutat
Dr. Da-Yan Liu
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

  • image processing
  • image fusion
  • image denoising
  • stability of fractional systems
  • control of fractional systems
  • singular fractional systems

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Related Special Issue

Published Papers (4 papers)

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Research

38 pages, 6851 KB  
Article
FGFNet: Fourier Gated Feature-Fusion Network with Fractal Dimension Estimation for Robust Palm-Vein Spoof Detection
by Seung Gu Kim, Jung Soo Kim and Kang Ryoung Park
Fractal Fract. 2025, 9(8), 478; https://doi.org/10.3390/fractalfract9080478 - 22 Jul 2025
Viewed by 369
Abstract
The palm-vein recognition system has garnered attention as a biometric technology due to its resilience to external environmental factors, protection of personal privacy, and low risk of external exposure. However, with recent advancements in deep learning-based generative models for image synthesis, the quality [...] Read more.
The palm-vein recognition system has garnered attention as a biometric technology due to its resilience to external environmental factors, protection of personal privacy, and low risk of external exposure. However, with recent advancements in deep learning-based generative models for image synthesis, the quality and sophistication of fake images have improved, leading to an increased security threat from counterfeit images. In particular, palm-vein images acquired through near-infrared illumination exhibit low resolution and blurred characteristics, making it even more challenging to detect fake images. Furthermore, spoof detection specifically targeting palm-vein images has not been studied in detail. To address these challenges, this study proposes the Fourier-gated feature-fusion network (FGFNet) as a novel spoof detector for palm-vein recognition systems. The proposed network integrates masked fast Fourier transform, a map-based gated feature fusion block, and a fast Fourier convolution (FFC) attention block with global contrastive loss to effectively detect distortion patterns caused by generative models. These components enable the efficient extraction of critical information required to determine the authenticity of palm-vein images. In addition, fractal dimension estimation (FDE) was employed for two purposes in this study. In the spoof attack procedure, FDE was used to evaluate how closely the generated fake images approximate the structural complexity of real palm-vein images, confirming that the generative model produced highly realistic spoof samples. In the spoof detection procedure, the FDE results further demonstrated that the proposed FGFNet effectively distinguishes between real and fake images, validating its capability to capture subtle structural differences induced by generative manipulation. To evaluate the spoof detection performance of FGFNet, experiments were conducted using real palm-vein images from two publicly available palm-vein datasets—VERA Spoofing PalmVein (VERA dataset) and PLUSVein-contactless (PLUS dataset)—as well as fake palm-vein images generated based on these datasets using a cycle-consistent generative adversarial network. The results showed that, based on the average classification error rate, FGFNet achieved 0.3% and 0.3% on the VERA and PLUS datasets, respectively, demonstrating superior performance compared to existing state-of-the-art spoof detection methods. Full article
(This article belongs to the Special Issue Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing​ Algorithms, Second Edition)
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18 pages, 451 KB  
Article
Distinctive LMI Formulations for Admissibility and Stabilization Algorithms of Singular Fractional-Order Systems with Order Less than One
by Xinhai Wang, Xuefeng Zhang, Qing-Guo Wang and Driss Boutat
Fractal Fract. 2025, 9(7), 470; https://doi.org/10.3390/fractalfract9070470 - 19 Jul 2025
Viewed by 292
Abstract
This paper presents three novel sufficient and necessary conditions for the admissibility of singular fractional-order systems (FOSs), a stabilization criterion, and a solution algorithm. The strict linear matrix inequality (LMI) stability criterion for integer-order systems is generalized to singular FOSs by using column-full [...] Read more.
This paper presents three novel sufficient and necessary conditions for the admissibility of singular fractional-order systems (FOSs), a stabilization criterion, and a solution algorithm. The strict linear matrix inequality (LMI) stability criterion for integer-order systems is generalized to singular FOSs by using column-full rank matrices. This admissibility criterion does not involve complex variables and is different from all previous results, filling a gap in this area. Based on the LMIs in the generalized condition, the improved criterion utilizes a variable substitution technique to reduce the number of matrix variables to be solved from one pair to one, reflecting the admissibility more essentially. This improved result simplifies the programming process compared to the traditional approach that requires two matrix variables. To complete the state feedback controller design, the system matrices in the generalized admissibility criterion are decoupled, but bilinear constraints still occur in the stabilization criterion. For this case, where a feasible solution cannot be found using the MATLAB LMI toolbox, a branch-and-bound algorithm (BBA) is designed to solve it. Finally, the validity of these criteria and the BBA is verified by three examples, including a real circuit model. Full article
(This article belongs to the Special Issue Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing​ Algorithms, Second Edition)
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26 pages, 23383 KB  
Article
Multi-Focus Image Fusion Based on Dual-Channel Rybak Neural Network and Consistency Verification in NSCT Domain
by Ming Lv, Sensen Song, Zhenhong Jia, Liangliang Li and Hongbing Ma
Fractal Fract. 2025, 9(7), 432; https://doi.org/10.3390/fractalfract9070432 - 30 Jun 2025
Cited by 5 | Viewed by 524
Abstract
In multi-focus image fusion, accurately detecting and extracting focused regions remains a key challenge. Some existing methods suffer from misjudgment of focus areas, resulting in incorrect focus information or the unintended retention of blurred regions in the fused image. To address these issues, [...] Read more.
In multi-focus image fusion, accurately detecting and extracting focused regions remains a key challenge. Some existing methods suffer from misjudgment of focus areas, resulting in incorrect focus information or the unintended retention of blurred regions in the fused image. To address these issues, this paper proposes a novel multi-focus image fusion method that leverages a dual-channel Rybak neural network combined with consistency verification in the nonsubsampled contourlet transform (NSCT) domain. Specifically, the high-frequency sub-bands produced by NSCT decomposition are processed using the dual-channel Rybak neural network and a consistency verification strategy, allowing for more accurate extraction and integration of salient details. Meanwhile, the low-frequency sub-bands are fused using a simple averaging approach to preserve the overall structure and brightness information. The effectiveness of the proposed method has been thoroughly evaluated through comprehensive qualitative and quantitative experiments conducted on three widely used public datasets: Lytro, MFFW, and MFI-WHU. Experimental results show that our method consistently outperforms several state-of-the-art image fusion techniques, including both traditional algorithms and deep learning-based approaches, in terms of visual quality and objective performance metrics (QAB/F, QCB, QE, QFMI, QMI, QMSE, QNCIE, QNMI, QP, and QPSNR). These results clearly demonstrate the robustness and superiority of the proposed fusion framework in handling multi-focus image fusion tasks. Full article
(This article belongs to the Special Issue Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing​ Algorithms, Second Edition)
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23 pages, 19331 KB  
Article
Multi-Focus Image Fusion Based on Fractal Dimension and Parameter Adaptive Unit-Linking Dual-Channel PCNN in Curvelet Transform Domain
by Liangliang Li, Sensen Song, Ming Lv, Zhenhong Jia and Hongbing Ma
Fractal Fract. 2025, 9(3), 157; https://doi.org/10.3390/fractalfract9030157 - 3 Mar 2025
Cited by 5 | Viewed by 925
Abstract
Multi-focus image fusion is an important method for obtaining fully focused information. In this paper, a novel multi-focus image fusion method based on fractal dimension (FD) and parameter adaptive unit-linking dual-channel pulse-coupled neural network (PAUDPCNN) in the curvelet transform (CVT) domain is proposed. [...] Read more.
Multi-focus image fusion is an important method for obtaining fully focused information. In this paper, a novel multi-focus image fusion method based on fractal dimension (FD) and parameter adaptive unit-linking dual-channel pulse-coupled neural network (PAUDPCNN) in the curvelet transform (CVT) domain is proposed. The source images are decomposed into low-frequency and high-frequency sub-bands by CVT, respectively. The FD and PAUDPCNN models, along with consistency verification, are employed to fuse the high-frequency sub-bands, the average method is used to fuse the low-frequency sub-band, and the final fused image is generated by inverse CVT. The experimental results demonstrate that the proposed method shows superior performance in multi-focus image fusion on Lytro, MFFW, and MFI-WHU datasets. Full article
(This article belongs to the Special Issue Fractional Order Complex Systems: Advanced Control, Intelligent Estimation and Reinforcement Learning Image Processing​ Algorithms, Second Edition)
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