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Fractal Fract
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Fractional Calculus Applications for Signal Processing and Data Science
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Fractional Calculus Applications for Signal Processing and Data Science

A special issue of Fractal and Fractional (ISSN 2504-3110).

Deadline for manuscript submissions: 15 February 2026 | Viewed by 735

Special Issue Editors

Prof. Dr. Héctor Vázquez-Leal

E-Mail Website
Guest Editor
Faculty of Electronic Instrumentation, Veracruz University, Veracruz 91000, Mexico
Interests: fractional calculus; approximate solutions development for nonlinear differential equations; numerical and computational methods; collision-free trajectory planning in robotics; techniques for electronic circuit simulation
Dr. Manuel Duarte Ortigueira

E-Mail Website
Guest Editor
CTS-UNINOVA and LASI, NOVA School of Science and Technology, NOVA University of Lisbon, Quinta da Torre, 2829-516 Caparica, Portugal
Interests: fractional calculus; signal processing; fractional signals and systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fractional calculus has gained significant interest in recent years, as scientists have continued to explore new scenarios for applying mathematical models derived from this unique branch of mathematics. In this context, the Special Issue "Fractional Calculus Applications for Signal Processing and Data Science" aims to showcase practical applications of fractional calculus across various fields, including signal processing, data science, machine learning, and related disciplines, hoping to shed light on traditional results that emerge as significant cases of back compatibility.

We highly encourage submissions that emphasize engineering applications where fractional calculus allows enlarging classic perspectives on signals and systems modeling/identification in time and frequency domains, image processing, fast numerical algorithms, data science tasks, and embedded systems. Submitted manuscripts must explain in detail the methodology that guarantees the reproducibility of the experiments described within the manuscript. Additionally, the materials needed to reproduce the achieved results should be available to readers either by default or upon request. Survey articles are welcome if they are written in a way that helps readers assess the role of fractional calculus in engineering applications.

Prof. Dr. Héctor Vázquez-Leal
Dr. Manuel Duarte Ortigueira
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
  • fractional transfer functions/Bode diagrams
  • fast numerical algorithms for fractional calculus
  • fractional signal processing in time and frequency domains
  • image processing and fractional techniques
  • embedded systems implementation of fractional operators
  • fractional filters design and implementation
  • fractional-order algorithms in AI
  • data science applications of fractional calculus
  • machine learning with fractional operators

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Published Papers (2 papers)

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31 pages, 6790 KiB  
Article
Proposal for the Application of Fractional Operators in Polynomial Regression Models to Enhance the Determination Coefficient R2 on Unseen Data
by Anthony Torres-Hernandez, Rafael Ramirez-Melendez and Fernando Brambila-Paz
Fractal Fract. 2025, 9(6), 393; https://doi.org/10.3390/fractalfract9060393 - 19 Jun 2025
Viewed by 51
Abstract
Since polynomial regression models are generally quite reliable for data that can be handled using a linear system, it is important to note that in some cases, they may suffer from overfitting during the training phase. This can lead to negative values of [...] Read more.
Since polynomial regression models are generally quite reliable for data that can be handled using a linear system, it is important to note that in some cases, they may suffer from overfitting during the training phase. This can lead to negative values of the coefficient of determination R2 when applied to unseen data. To address this issue, this work proposes the partial implementation of fractional operators in polynomial regression models to construct a fractional regression model. The aim of this approach is to mitigate overfitting, which could potentially improve the R2 value for unseen data compared to the conventional polynomial model, under the assumption that this could lead to predictive models with better performance. The methodology for constructing these fractional regression models is presented along with examples applicable to both Riemann–Liouville and Caputo fractional operators, where some results show that regions with initially negative or near-zero R2 values exhibit remarkable improvements after the application of the fractional operator, with absolute relative increases exceeding 800% on unseen data. Finally, the importance of employing sets in the construction of the fractional regression model within this methodological framework is emphasized, since from a theoretical standpoint, one could construct an uncountable family of fractional operators derived from the Riemann–Liouville and Caputo definitions that, although differing in their formulation, would yield the same regression results as those shown in the examples presented in this work. Full article
(This article belongs to the Special Issue Fractional Calculus Applications for Signal Processing and Data Science)
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21 pages, 2835 KiB  
Article
Deep Learning for Leukemia Classification: Performance Analysis and Challenges Across Multiple Architectures
by Hari Mohan Rai, B. Omkar Lakshmi Jagan, N. Thiruapthi Rao, Thayyaba Khatoon Mohammed, Neha Agarwal, Hanaa A. Abdallah and Saurabh Agarwal
Fractal Fract. 2025, 9(6), 337; https://doi.org/10.3390/fractalfract9060337 - 23 May 2025
Viewed by 468
Abstract
Leukemia is a very heterogeneous and complex blood cancer, which poses a significant challenge in its proper categorization and diagnosis. This paper aims to introduce various deep learning architectures, namely EfficientNet, LeNet, AlexNet, ResNet, VGG, and custom CNNs, for improved classification of leukemia [...] Read more.
Leukemia is a very heterogeneous and complex blood cancer, which poses a significant challenge in its proper categorization and diagnosis. This paper aims to introduce various deep learning architectures, namely EfficientNet, LeNet, AlexNet, ResNet, VGG, and custom CNNs, for improved classification of leukemia subtypes. These models provide much improvement in feature extraction and learning, which further helps in the performance and reliability of classification. A web-based interface has also been provided through which a user can upload images and clinical data for analysis. The interface displays model predictions, symptom analysis, and accuracy metrics. Data collection, preprocessing, normalization, and scaling are part of the framework, considering leukemia cell images, genomic features, and clinical records. Using the preprocessed data, training is performed on the various models with thorough testing and validation to fine-tune the best-performing architecture. Among these, AlexNet gave a classification accuracy of 88.975%. These results strongly underscore the potential of advanced deep learning techniques to radically transform leukemia diagnosis and classification for precision medicine. Full article
(This article belongs to the Special Issue Fractional Calculus Applications for Signal Processing and Data Science)
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