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Mathematics
Special Issues
Advances in Fractional Order Models and Applications
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Advances in Fractional Order Models and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 10 March 2026 | Viewed by 268

Special Issue Editor

Dr. Yuan-Min Li

E-Mail Website
Guest Editor
School of Mathematics and Statistics, Xidian University, Xi'an 710071, China
Interests: fractional Fourier transform; sparse optimization; cone and stochastic optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Compared to integer-order systems, fractional-order models and systems have more advantages. Due to the introduction of more degrees of freedom in fractional-order models, model parameters can be adjusted more flexibly and the dynamic characteristics of systems can generally be described more accurately compared to integer-order models. The fractional-order model can better describe the memory effect and genetic characteristics of the system. These models are usually better in demonstrating robustness than integer-order models are. Therefore, the fields of application of fractional-order models are very extensive, including fluid mechanics, the anomalous diffusion and heat conduction of matter and biology, signal and image processing (especially magnetic resonance imaging), system control, fractional-order PID controllers, fractal theory, and so on.

This Special Issue aims to continue the research on the theory of fractional-order models and their related applications. The topics invited for submission include (but are not limited to) the following:

  • Fractional-order dynamical systems and their applications;
  • Fractional-order delayed dynamical systems and their applications;
  • Fractional-order partial differential equations;
  • Fractional-order transform and its applications in signal and imaging processing;
  • Fractional-order control systems;
  • Uncertain fractional-order systems;
  • Neurodynamic and fractional-order neurodynamic models;
  • Fractional-order optimization.

Dr. Yuan-Min Li
Guest Editor

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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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 delayed dynamical systems
  • fractional-order partial differential equations
  • fractional-order optimization
  • fractional-order transform
  • fractional-order dynamical systems
  • fractional-order control systems
  • fractional-order neurodynamic models

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Published Papers (1 paper)

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Research

31 pages, 1473 KB  
Article
Integrating Fractional Calculus Memory Effects and Laguerre Polynomial in Secretary Bird Optimization for Gene Expression Feature Selection
by Islam S. Fathi, Ahmed R. El-Saeed, Hanin Ardah, Mohammed Tawfik and Gaber Hassan
Mathematics 2025, 13(21), 3511; https://doi.org/10.3390/math13213511 - 2 Nov 2025
Viewed by 86
Abstract
Feature selection in high-dimensional datasets presents significant computational challenges, particularly in domains with large feature spaces and limited sample sizes. This paper introduces FL-SBA, a novel metaheuristic algorithm integrating fractional calculus enhancements with Laguerre operators into the Secretary Bird Optimization Algorithm framework for [...] Read more.
Feature selection in high-dimensional datasets presents significant computational challenges, particularly in domains with large feature spaces and limited sample sizes. This paper introduces FL-SBA, a novel metaheuristic algorithm integrating fractional calculus enhancements with Laguerre operators into the Secretary Bird Optimization Algorithm framework for binary feature selection. The methodology incorporates fractional opposition-based learning utilizing Laguerre operators for enhanced population initialization with non-local memory characteristics, and a Laguerre-based binary transformation function replacing conventional sigmoid mechanisms through orthogonal polynomial approximation. Fractional calculus integration introduces memory effects that enable historical search information retention, while Laguerre polynomials provide superior approximation properties and computational stability. Comprehensive experimental validation across ten high-dimensional gene expression datasets compared FL-SBA against standard SBA and five contemporary methods including BinCOA, BAOA, BJSO, BGWO, and BMVO. Results demonstrate FL-SBA’s superior performance, achieving 96.06% average classification accuracy compared to 94.41% for standard SBA and 82.91% for BinCOA. The algorithm simultaneously maintained exceptional dimensionality reduction efficiency, selecting 29 features compared to 40 for competing methods, representing 27% improvement while achieving higher accuracy. Statistical analysis reveals consistently lower fitness values (0.04924 averages) and stable performance with minimal standard deviation. The integration addresses fundamental limitations in integer-based computations while enhancing convergence behavior. These findings suggest FL-SBA represents significant advancement in metaheuristic-based feature selection, offering theoretical innovation and practical performance improvements for high-dimensional optimization challenges. Full article
(This article belongs to the Special Issue Advances in Fractional Order Models and Applications)
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