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Recent Advances in Fractional-Order Neural Networks: Theory and Application, 2nd...
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Recent Advances in Fractional-Order Neural Networks: Theory and Application, 2nd Edition

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

Deadline for manuscript submissions: 25 May 2025 | Viewed by 1586

Special Issue Editors

Prof. Dr. Zhouchao Wei

E-Mail Website
Guest Editor
School of Mathematics and Physics, China University of Geosciences (Wuhan), Wuhan 430074, China
Interests: chaos theory; bifurcation; hidden attractors; non-smooth systems
Special Issues, Collections and Topics in MDPI journals
Dr. Lulu Lu

E-Mail Website
Guest Editor
School of Mathematics and Physics, China University of Geosciences (Wuhan), Wuhan 430074, China
Interests: computational neuroscience; system biology
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The field of fractional-order neural networks refers to research that incorporates the concepts of fractional calculus into the related theory and application of neural networks. It is introduced to accurately describe the physical process and system state with heredity and memorability. With the in-depth study of fractional-order neural network models and dynamics analysis (e.g., stability, synchronization, bifurcation, etc.), more control methods and control techniques are applied to these systems, which will enrich the theoretical system of fractional-order neural networks. Additionally, fractional-order neural networks have infinite memory properties, which can further improve the design, characterization, and control capabilities of network models for many practical problems. These concepts have great application prospects and research value in biological nervous systems, circuit design and simulation, artificial intelligence, and other fields.

The focus of this Special Issue is to continue to advance research on topics relating to the theory, control, design, and application of fractional-order neural networks. Topics that are invited for submission include (but are not limited to):

  • Fractional-order neural network model;
  • Dynamic analysis and control of fractional-order neural networks;
  • Circuit design and simulation of fractional-order neural networks;
  • Applications of fractional-order neural networks for biology and biomedicine;
  • Applications of fractional-order circuit models for artificial intelligence.

Please feel free to read and download all our published papers in the first volume:

https://www.mdpi.com/journal/fractalfract/special_issues/RAFONNTA

Prof. Dr. Zhouchao Wei
Dr. Lulu Lu
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 calculus
  • dynamics analysis
  • biological nervous system
  • circuit design and simulation
  • artificial intelligence

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Related Special Issue

Published Papers (2 papers)

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Research

38 pages, 16379 KiB  
Article
Hyperbolic Sine Function Control-Based Finite-Time Bipartite Synchronization of Fractional-Order Spatiotemporal Networks and Its Application in Image Encryption
by Lvming Liu, Haijun Jiang, Cheng Hu, Haizheng Yu, Siyu Chen, Yue Ren, Shenglong Chen and Tingting Shi
Fractal Fract. 2025, 9(1), 36; https://doi.org/10.3390/fractalfract9010036 - 13 Jan 2025
Viewed by 474
Abstract
This work is devoted to the hyperbolic sine function (HSF) control-based finite-time bipartite synchronization of fractional-order spatiotemporal networks and its application in image encryption. Initially, the addressed networks adequately take into account the nature of anisotropic diffusion, i.e., the diffusion matrix can be [...] Read more.
This work is devoted to the hyperbolic sine function (HSF) control-based finite-time bipartite synchronization of fractional-order spatiotemporal networks and its application in image encryption. Initially, the addressed networks adequately take into account the nature of anisotropic diffusion, i.e., the diffusion matrix can be not only non-diagonal but also non-square, without the conservative requirements in plenty of the existing literature. Next, an equation transformation and an inequality estimate for the anisotropic diffusion term are established, which are fundamental for analyzing the diffusion phenomenon in network dynamics. Subsequently, three control laws are devised to offer a detailed discussion for HSF control law’s outstanding performances, including the swifter convergence rate, the tighter bound of the settling time and the suppression of chattering. Following this, by a designed chaotic system with multi-scroll chaotic attractors tested with bifurcation diagrams, Poincaré map, and Turing pattern, several simulations are pvorided to attest the correctness of our developed findings. Finally, a formulated image encryption algorithm, which is evaluated through imperative security tests, reveals the effectiveness and superiority of the obtained results. Full article
(This article belongs to the Special Issue Recent Advances in Fractional-Order Neural Networks: Theory and Application, 2nd Edition)
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17 pages, 3382 KiB  
Article
Optimizing Fractional-Order Convolutional Neural Networks for Groove Classification in Music Using Differential Evolution
by Jiangang Chen, Pei Su, Daxin Li, Junbo Han, Gaoquan Zhou and Donghui Tang
Fractal Fract. 2024, 8(11), 616; https://doi.org/10.3390/fractalfract8110616 - 23 Oct 2024
Viewed by 876
Abstract
This study presents a differential evolution (DE)-based optimization approach for fractional-order convolutional neural networks (FOCNNs) aimed at enhancing the accuracy of groove classification in music. Groove, an essential element in music perception, is typically influenced by rhythmic patterns and acoustic features. While FOCNNs [...] Read more.
This study presents a differential evolution (DE)-based optimization approach for fractional-order convolutional neural networks (FOCNNs) aimed at enhancing the accuracy of groove classification in music. Groove, an essential element in music perception, is typically influenced by rhythmic patterns and acoustic features. While FOCNNs offer a promising method for capturing these subtleties through fractional-order derivatives, they face challenges in efficiently converging to optimal parameters. To address this, DE is applied to optimize the initial weights and biases of FOCNNs, leveraging its robustness and ability to explore a broad solution space. The proposed DE-FOCNN was evaluated on the Janata dataset, which includes pre-rated music tracks. Comparative experiments across various fractional-order values demonstrated that DE-FOCNN achieved superior performance in terms of higher test accuracy and reduced overfitting compared to a standard FOCNN. Specifically, DE-FOCNN showed optimal performance at fractional-order values such as v = 1.4. Further experiments demonstrated that DE-FOCNN achieved higher accuracy and lower variance compared to other popular evolutionary algorithms. This research primarily contributes to the optimization of FOCNNs by introducing a novel DE-based approach for the automated analysis and classification of musical grooves. The DE-FOCNN framework holds promise for addressing other related engineering challenges. Full article
(This article belongs to the Special Issue Recent Advances in Fractional-Order Neural Networks: Theory and Application, 2nd Edition)
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