Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.6
3.6
Journals
Fractal Fract
Special Issues
Applied Fractional Calculus in Machine Learning and Biomedical Engineering
share announcement

Applied Fractional Calculus in Machine Learning and Biomedical Engineering

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Optimization, Big Data, and AI/ML".

Deadline for manuscript submissions: 31 October 2025 | Viewed by 1019

Special Issue Editor

Dr. Saptarshi Das

E-Mail Website
Guest Editor
Centre for Environmental Mathematics, Faculty of Environment, Science and Economy, University of Exeter, Penryn Campus, Cornwall TR10 9FE, UK
Interests: dynamical systems; systems and control theory; fractional calculus; computational intelligence; optimization; signal processing; machine learning; energy and power engineering; biomedical engineering; data science

Special Issue Information

Dear Colleagues,

The application of fractional calculus in machine learning and biomedical engineering is a novel and rapidly growing area of research. The non-integer-order differentiation and integration offered by FC allow for more accurate modelling of dynamical systems with memory and hereditary properties, which are common in biological systems and complex datasets.

The intersection of FC with ML and BME is an emerging field that promises to revolutionize the way we approach problems in data analysis, signal processing, biomedical system modelling, and control. This Special Issue will provide a comprehensive platform for researchers to present their latest theoretical advances, innovative applications, and practical implementations of FC in these domains.

This special issue aims to bring together cutting-edge research and developments in the application of fractional calculus (FC) to the fields of machine learning (ML) and biomedical engineering (BME). Fractional calculus, an extension of traditional integer-order calculus, offers a powerful framework for describing anomalous dynamics and complex systems. Its non-local and memory-preserving properties have shown significant potential in modelling and solving complex problems that are otherwise intractable with traditional integer-order methods.

  • Theoretical advances in fractional calculus and their implications for ML and BME.
  • Development of fractional-order algorithms for machine learning models.
  • Application of FC in the design of neural networks, including deep learning and reinforcement learning.
  • Fractional-order systems in biomedical signal processing and image analysis.
  • Modelling of biological systems using fractional-order differential equations (FODEs).
  • Fractional-order control systems in biomedical devices and robotics.
  • Applications of fractional calculus in physiological modelling and bioinformatics.
  • Challenges and future directions in the integration of FC with ML and BME.

The Special Issue targets a multidisciplinary audience that includes researchers, academicians, and professionals working in the fields of applied mathematics, machine learning, biomedical engineering, and systems biology. It will also be of interest to practitioners who are looking to apply fractional calculus methods to solve practical problems in ML and BME.

Dr. Saptarshi Das
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. 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 machine learning algorithms
  • application of fractional calculus in deep learning, including novel architectures and training methods
  • fractional calculus in biomedical signal processing (EEG, ECG, MRI, etc.)
  • modelling of biological phenomena using fractional differential equations
  • fractional-order control systems in biomedical devices
  • fractional calculus in the analysis of biomedical data and its integration with ML techniques
  • comparative studies between integer-order and fractional-order methods in ML and BME
  • practical challenges in applying FC to real-world problems in ML and BME

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

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

Published Papers (1 paper)

Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

24 pages, 28364 KiB  
Article
Uncertainty-Aware Self-Attention Model for Time Series Prediction with Missing Values
by Jiabao Li, Chengjun Wang, Wenhang Su, Dongdong Ye and Ziyang Wang
Fractal Fract. 2025, 9(3), 181; https://doi.org/10.3390/fractalfract9030181 - 16 Mar 2025
Viewed by 477
Abstract
Missing values in time series data present a significant challenge, often degrading the performance of downstream tasks such as classification and forecasting. Traditional approaches address this issue by first imputing the missing values and then independently solving the predictive tasks. Recent methods have [...] Read more.
Missing values in time series data present a significant challenge, often degrading the performance of downstream tasks such as classification and forecasting. Traditional approaches address this issue by first imputing the missing values and then independently solving the predictive tasks. Recent methods have leveraged self-attention models to enhance imputation quality and accelerate inference. These models, however, predict values based on all input observations—including the missing values—thereby potentially compromising the fidelity of the imputed data. In this paper, we propose the Uncertainty-Aware Self-Attention (UASA) model to overcome these limitations. Our approach introduces two novel techniques: (i) A self-attention mechanism with a partially observed diagonal that effectively captures complex non-local dependencies in time series data—a characteristic also observed in fractional-order systems. This approach draws inspiration from fractional calculus, where non-integer-order derivatives better characterize complex dynamical systems with long-memory effects, providing a more comprehensive mathematical framework for handling temporal data. And (ii) uncertainty quantification in data imputation to better inform downstream tasks. The UASA model comprises an upstream component for data imputation and a downstream component for time series prediction, trained jointly in an end-to-end fashion to optimize both imputation accuracy and task-specific objectives simultaneously. For classification tasks, the UASA model demonstrates remarkable performance even under high missing data rates, achieving a ROC-AUC of 99.5%, a PR-AUC of 58.5%, and an F1-SCORE of 49.3%. For forecasting tasks on the AUST-Gait dataset, the UASA model achieves a Mean Squared Error (MSE) of 0.72 under 0% missing data conditions (i.e., complete data input). Under the end-to-end training strategy evaluated across all missing data rates, the model achieves an average MSE of 0.74, showcasing its adaptability and robustness across diverse missing data scenarios. Full article
(This article belongs to the Special Issue Applied Fractional Calculus in Machine Learning and Biomedical Engineering)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-1
Back to TopTop