Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.6
2.2
Journals
Mathematics
Special Issues
Fractional Order Systems and Its Applications
share announcement

Fractional Order Systems and Its Applications

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

Deadline for manuscript submissions: 30 November 2026 | Viewed by 3524

Special Issue Editors

Dr. Ricardo Cajo Diaz

E-Mail Website
Guest Editor
Research Group on Industrial Automation and Control, Department of Electronics and Automation Engineering, Escuela Superior Politecnica del Litoral, ESPOL, Gustavo Galindo Km 30.5 Vía Perimetral, P.O. Box 09-01-5863, Guayaquil, Ecuador
Interests: fractional calculus; control system optimization: autonomous vehicles and multi-agent systems
Special Issues, Collections and Topics in MDPI journals
Dr. Isabela Roxana Birs

E-Mail Website
Guest Editor
1. Research Group of Dynamical Systems and Control, Faculty of Engineering and Architecture, Ghent University, Technologiepark 125, B-9052 Ghent, Belgium
2. Automation Department, Technical University of Cluj-Napoca, Memorandumului 28, 400114 Cluj-Napoca, Romania
Interests: fractional calculus; fractional order control; biomedical systems; vibration suppression; non-Newtonian models
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The Special Issue on “Fractional Order Systems and Its Applications” invites high-quality research contributions in the growing field of fractional calculus and its diverse engineering and scientific applications. Fractional order systems, defined by derivatives and integrals of non-integer order, offer enhanced modeling capabilities for systems with memory and hereditary properties, outperforming traditional integer-order models in many cases.

This Special Issue welcomes original research, reviews, and case studies addressing theoretical advances, numerical techniques, control approaches, and practical implementations. We especially encourage interdisciplinary works demonstrating the effectiveness of fractional models in areas such as control engineering, signal processing, biomedical systems, robotics, and complex dynamics.

Topics of interest include, but are not limited to:

  • Mathematical foundations and modeling of fractional systems
  • Stability, simulation, and control strategies
  • Fractional order controllers (e.g., PID, sliding mode, adaptive)
  • Optimization methods and algorithm design
  • Applications in electrical, mechanical, thermal, and biomedical systems
  • Signal and image processing
  • Robotics and automation
  • Embedded system implementation
  • Software/hardware tools for fractional system analysis

We look forward to your valuable contributions to advance this exciting and impactful area of research.

Dr. Ricardo Cajo Diaz
Dr. Isabela Roxana Birs
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. 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 calculus
  • fractional order modelling
  • fractional control
  • memory effects
  • non-integer dynamics
  • applications of fractional systems
  • system identification
  • robust control

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 (2 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

Jump to: Review

27 pages, 4240 KB  
Article
Robust State Estimation of Power System Based on Unscented Kalman Filter with Fractional-Order Adaptive Generalized Cross Correlation Entropy
by Yan Huang, Shangyong Wen, Hongyan Xin and Chaohui Xin
Mathematics 2026, 14(4), 642; https://doi.org/10.3390/math14040642 - 12 Feb 2026
Viewed by 370
Abstract
With the high penetration of power electronic devices, modern power systems exhibit complex fractional-order dynamic characteristics. Addressing this, along with the prevalent issues of multi-modal non-Gaussian noise, outliers, and sudden load changes, a fractional-order adaptive generalized cross correlation entropy unscented Kalman filter (FO-AGCCE-UKF) [...] Read more.
With the high penetration of power electronic devices, modern power systems exhibit complex fractional-order dynamic characteristics. Addressing this, along with the prevalent issues of multi-modal non-Gaussian noise, outliers, and sudden load changes, a fractional-order adaptive generalized cross correlation entropy unscented Kalman filter (FO-AGCCE-UKF) method is proposed in this paper. First, acknowledging that traditional integer-order models overlook the cumulative effects of historical states, a fractional-order (FO) discrete-time state-space model is constructed based on the Grünwald–Letnikov definition. This model accurately characterizes the long-memory and non-locality properties of power systems, thereby improving modeling accuracy during transient processes. Second, to mitigate the impact of non-Gaussian noise and outliers, the generalized cross correlation entropy (GCCE) criterion is adopted to replace the traditional mean square error (MSE) criterion. Combined with statistical linearization techniques, a novel recursive filtering framework is derived to enhance robustness against heavy-tailed noise. Furthermore, to address the time-varying and unknown statistical properties of process and measurement noise, an adaptive update mechanism for noise covariance matrices is introduced, which corrects noise parameters online based on innovation sequences. Simulation experiments and comparative analysis on multiple power systems of different scales demonstrate that the proposed method not only exhibits superior anti-interference capability in mixed-Gaussian noise environments but also achieves a faster convergence speed and higher tracking accuracy during dynamic events such as sudden load changes. Full article
(This article belongs to the Special Issue Fractional Order Systems and Its Applications)
►▼ Show Figures

Figure 1

Review

Jump to: Research

34 pages, 2714 KB  
Review
The Role of Fractional Calculus in Modern Optimization: A Survey of Algorithms, Applications, and Open Challenges
by Edson Fernandez, Victor Huilcapi, Isabela Birs and Ricardo Cajo
Mathematics 2025, 13(19), 3172; https://doi.org/10.3390/math13193172 - 3 Oct 2025
Cited by 9 | Viewed by 2612
Abstract
This paper provides a comprehensive overview of the application of fractional calculus in modern optimization methods, with a focus on its impact in artificial intelligence (AI) and computational science. We examine how fractional-order derivatives have been integrated into traditional methodologies, including gradient descent, [...] Read more.
This paper provides a comprehensive overview of the application of fractional calculus in modern optimization methods, with a focus on its impact in artificial intelligence (AI) and computational science. We examine how fractional-order derivatives have been integrated into traditional methodologies, including gradient descent, least mean squares algorithms, particle swarm optimization, and evolutionary methods. These modifications leverage the intrinsic memory and nonlocal features of fractional operators to enhance convergence, increase resilience in high-dimensional and non-linear environments, and achieve a better trade-off between exploration and exploitation. A systematic and chronological analysis of algorithmic developments from 2017 to 2025 is presented, together with representative pseudocode formulations and application cases spanning neural networks, adaptive filtering, control, and computer vision. Special attention is given to advances in variable- and adaptive-order formulations, hybrid models, and distributed optimization frameworks, which highlight the versatility of fractional-order methods in addressing complex optimization challenges in AI-driven and computational settings. Despite these benefits, persistent issues remain regarding computational overhead, parameter selection, and rigorous convergence analysis. This review aims to establish both a conceptual foundation and a practical reference for researchers seeking to apply fractional calculus in the development of next-generation optimization algorithms. Full article
(This article belongs to the Special Issue Fractional Order Systems and Its Applications)
►▼ Show Figures

Figure 1

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-2
Back to TopTop