Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
6.0
3.3
Journals
Fractal Fract
Special Issues
Data-Driven Modeling, Prediction and Control of Fractional-Order Systems
share announcement

Data-Driven Modeling, Prediction and Control of Fractional-Order Systems

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: 30 May 2026 | Viewed by 2606

Special Issue Editors

Dr. Fudong Ge

E-Mail Website
Guest Editor
School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China
Interests: distributed actuation and distributed sensing; regional sensing and actuation; data-driven modeling and analysis
Special Issues, Collections and Topics in MDPI journals
Dr. Ying Luo

E-Mail Website
Guest Editor
School of Automation Science and Engineering, South China University and Technology, Guangzhou 510641, China
Interests: fractional-order systems modeling and controls; data-driving servo systems; industrial and intelligent robots
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Yangquan Chen

grade E-Mail Website
Guest Editor
Department of Mechanical Engineering (ME), University of California, Merced, CA 95343, USA
Interests: data-driven modeling, learning, and optimization; control theory of fractional systems and their applications; distributed measurement and distributed control; signal processing
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Over the past few decades, the modeling, analysis, and control of fractional-order systems have attracted considerable attention and shown the increasingly important role of fractional calculus in various science and engineering fields. Fractional-order systems are believed to offer significant advantages over integer-order dynamics in our real-world applications. Moreover, as is well-known, data-driven discovery has revolutionized how we model, predict, and control complex systems. With modern mathematical methods, enabled by the unprecedented availability of data and computational resources, data-driven modeling, prediction, and control of fractional-order systems, can then allow us to obtain more adaptive, efficient, and intelligent results compared to the available studies and to also tackle previously unattainable problems. A collocation of the recent developments on the modeling, analysis, and control methods of fractional-order systems and their applications would be both challenging and significant.

The aim of this Special Issue is to show the control engineering research community the usefulness of the data-driven discovery of fractional-order systems, ranging from modeling to control prediction. It is our sincere hope that this Special Issue can show the important theoretical significance and practical values of data-driven modeling, prediction, and control of complex systems, and inspire further research of this topic.

Topics of this Special Issue include, but are not limited to, the following:

  • Data-driven modeling and identification for fractional-order ODE/PDE systems;
  • Data-driven learning and prediction of fractional-order ODE/PDE systems;
  • Data-driven controller design for fractional-order ODE/PDE systems;
  • Data-driven optimal control of fractional-order ODE/PDE systems;
  • The applications of advanced fractional data-driven modeling, prediction, and control methods in climate, epidemiology, finance, robotics, turbulence, etc.

We look forward to your contributions.

Dr. Fudong Ge
Dr. Ying Luo
Prof. Dr. Yangquan Chen
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 250 words) can be sent to the Editorial Office for assessment.

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 systems
  • fractional-order ODE systems
  • fractional-order PDE systems
  • data-driven modeling and identification
  • data-driven learning and prediction
  • data-driven controller design
  • artificial intelligence/machine learning

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.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

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

Published Papers (3 papers)

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

Research

18 pages, 3659 KB  
Article
On Estimation of α-Stable Distribution Using L-Moments
by Xunzhi Liao and Paweł D. Domański
Fractal Fract. 2025, 9(11), 711; https://doi.org/10.3390/fractalfract9110711 - 4 Nov 2025
Viewed by 718
Abstract
The family of stable distributions and, in particular, the α-stable distribution increases its applicability in engineering sciences. Examination of industrial data shows that originally assumed Gaussian properties are not so often observed. Research shows that stable functions can cover much wider spectrum [...] Read more.
The family of stable distributions and, in particular, the α-stable distribution increases its applicability in engineering sciences. Examination of industrial data shows that originally assumed Gaussian properties are not so often observed. Research shows that stable functions can cover much wider spectrum of cases. However, the estimations of α-stable distribution factors may pose some limitations. One of the control engineering aspects, i.e., the assessment of controller performance, may be successfully addressed by L-moments and L-moment ratio diagrams (LMRD). Simultaneously, LMRDs are often used as a method for distribution, fitting with the method of moments (MOM). Unfortunately, the moments do not exist for α-stable distribution. This research shows that, with the use of a Monte-Carlo analysis, this limitation may be overcome, and an efficient method to estimate statistical factors of the α-stable distribution is proposed. Full article
(This article belongs to the Special Issue Data-Driven Modeling, Prediction and Control of Fractional-Order Systems)
►▼ Show Figures

Figure 1

27 pages, 624 KB  
Article
Empirical Comparison of Neural Network Architectures for Prediction of Software Development Effort and Duration
by Anca-Elena Iordan
Fractal Fract. 2025, 9(11), 702; https://doi.org/10.3390/fractalfract9110702 - 31 Oct 2025
Viewed by 912
Abstract
Accurately estimating the effort and duration required for software development is one of the most important challenges in the field of software engineering. In a context where software projects are becoming increasingly complex, project managers face real difficulties in meeting established deadlines and [...] Read more.
Accurately estimating the effort and duration required for software development is one of the most important challenges in the field of software engineering. In a context where software projects are becoming increasingly complex, project managers face real difficulties in meeting established deadlines and staying within budget constraints. The purpose of this research study is to identify which type of artificial neural network is most suitable for estimating the effort and duration of software development, given the relatively small size of existing datasets. In the process of software effort and duration prediction, four datasets were used: China, Desharnais, Kemerer and Maxwell. Additionally, different types of artificial neural networks were used: Multilayer Perceptron, Fractal Neural Network, Deep Fully Connected Neural Network, Extreme Learning Machine, and Hybrid Neural Network. Another goal of this research is to analyze the impact of a new and innovative hybrid architecture, which combines Fractal Neural Network with Random Forests in the estimation process. Five metrics were used to compare the accuracy of artificial neural networks: mean absolute error, median absolute error, root mean square error, coefficient of determination, and mean squared logarithmic error. Python 3.11 programming language was used in combination with TensorFlow, Keras, and Scikit-learn libraries to implement artificial neural networks. Full article
(This article belongs to the Special Issue Data-Driven Modeling, Prediction and Control of Fractional-Order Systems)
►▼ Show Figures

Figure 1

41 pages, 12462 KB  
Article
Real-Time Efficient Approximation of Nonlinear Fractional-Order PDE Systems via Selective Heterogeneous Ensemble Learning
by Biao Ma and Shimin Dong
Fractal Fract. 2025, 9(10), 660; https://doi.org/10.3390/fractalfract9100660 - 13 Oct 2025
Viewed by 469
Abstract
Rod-pumping systems represent complex nonlinear systems. Traditional soft-sensing methods used for efficiency prediction in such systems typically rely on complicated fractional-order partial differential equations, severely limiting the real-time capability of efficiency estimation. To address this limitation, we propose an approximate efficiency prediction model [...] Read more.
Rod-pumping systems represent complex nonlinear systems. Traditional soft-sensing methods used for efficiency prediction in such systems typically rely on complicated fractional-order partial differential equations, severely limiting the real-time capability of efficiency estimation. To address this limitation, we propose an approximate efficiency prediction model for nonlinear fractional-order differential systems based on selective heterogeneous ensemble learning. This method integrates electrical power time-series data with fundamental operational parameters to enhance real-time predictive capability. Initially, we extract critical parameters influencing system efficiency using statistical principles. These primary influencing factors are identified through Pearson correlation coefficients and validated using p-value significance analysis. Subsequently, we introduce three foundational approximate system efficiency models: Convolutional Neural Network-Echo State Network-Bidirectional Long Short-Term Memory (CNN-ESN-BiLSTM), Bidirectional Long Short-Term Memory-Bidirectional Gated Recurrent Unit-Transformer (BiLSTM-BiGRU-Transformer), and Convolutional Neural Network-Echo State Network-Bidirectional Gated Recurrent Unit (CNN-ESN-BiGRU). Finally, to balance diversity among basic approximation models and predictive accuracy, we develop a selective heterogeneous ensemble-based approximate efficiency model for nonlinear fractional-order differential systems. Experimental validation utilizing actual oil-well parameters demonstrates that the proposed approach effectively and accurately predicts the efficiency of rod-pumping systems. Full article
(This article belongs to the Special Issue Data-Driven Modeling, Prediction and Control of Fractional-Order Systems)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-3
Back to TopTop