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Fractal Fract
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Recent Advances in Fractional-Order Equations and Their Applications in Modern...
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Recent Advances in Fractional-Order Equations and Their Applications in Modern Energy Systems

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: 15 July 2025 | Viewed by 2429

Special Issue Editors

Dr. Zhe Gao

E-Mail Website
Guest Editor
Department of Electrical Engineering and Automation, College of Light Industry, Liaoning University, Shenyang 110036, China
Interests: analysis and control of fractional-order systems; fractional-order model for power batteries; deep learning and intelligent computing
Dr. Xiaoting Gao

E-Mail Website
Guest Editor
College of Light Industry, Liaoning University, Shenyang 110036, China
Interests: nonlinear control; fractional-order systems; prescribed performance control; fractional-order modeling of active magnetic bearings
Dr. Enchang Cui

E-Mail Website
Guest Editor
College of Light Industry, Liaoning University, Shenyang 110036, China
Interests: nonlinear systems; fractional-order systems; nonlinear control; prescribed performance control

Special Issue Information

Dear Colleagues,

Fractional-order equations have emerged as a powerful mathematical tool in recent years, offering unique insights and solutions to a wide range of problems across various fields. This Special Issue aims to explore the latest developments, methodologies, and applications of fractional-order equations, particularly in the field of modern energy systems. On account of the ability to model complex dynamical systems more accurately than conventional integer-order equations, fractional-order equations present several advantages regarding modern energy systems. For instance, fractional-order models can accurately capture the inherent intermittency and variability in renewable resources, such as solar photovoltaic arrays and wind turbines. Moreover, fractional-order models offer a more nuanced representation of electrochemical processes, diffusion phenomena, and degradation mechanisms in energy storage systems, such as batteries and supercapacitors. 

The purpose of this Special Issue is to continue to provide a platform to share the insights, findings, and experiences in utilizing fractional-order equations to address the challenges and opportunities in modern energy systems. Topics that are invited for submission may include, but are not limited to, the following:

  • Fractional-order control theory in modern energy systems;
  • Theoretical frameworks and foundations of fractional-order equations in modern energy systems;
  • Fractional-order modeling and analysis of modern energy systems;
  • Fractional-order control systems and implementation of modern energy systems;
  • Applications of fractional-order equations in renewable energy sources;
  • Fractional-order control and optimization of energy systems;
  • Fractional-order dynamics in energy storage and energy conversion systems;
  • Case studies and implementations of fractional-order models in energy systems;
  • Energy storage systems, supercapacitors and batteries, and hybrid energy storage.

Dr. Zhe Gao
Dr. Xiaoting Gao
Dr. Enchang Cui
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-order control theory in modern energy systems
  • theoretical frameworks and foundations of fractional-order equations in modern energy systems
  • fractional-order modeling and analysis of modern energy systems
  • fractional-order control systems and implementation of modern energy systems
  • applications of fractional-order equations in renewable energy sources
  • fractional-order control and optimization of energy systems
  • fractional-order dynamics in energy storage and energy conversion systems
  • case studies and implementations of fractional-order models in energy systems
  • energy storage systems, supercapacitors and batteries, and hybrid energy storage

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  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
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Further information on MDPI's Special Issue policies can be found here.

Published Papers (2 papers)

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Research

23 pages, 13775 KiB  
Article
Physics-Informed Fractional-Order Recurrent Neural Network for Fast Battery Degradation with Vehicle Charging Snippets
by Yanan Wang, Min Wei, Feng Dai, Daijiang Zou, Chen Lu, Xuebing Han, Yangquan Chen and Changwei Ji
Fractal Fract. 2025, 9(2), 91; https://doi.org/10.3390/fractalfract9020091 - 1 Feb 2025
Viewed by 633
Abstract
To handle and manage battery degradation in electric vehicles (EVs), various capacity estimation methods have been proposed and can mainly be divided into traditional modeling methods and data-driven methods. For realistic conditions, data-driven methods take the advantage of simple application. However, state-of-the-art machine [...] Read more.
To handle and manage battery degradation in electric vehicles (EVs), various capacity estimation methods have been proposed and can mainly be divided into traditional modeling methods and data-driven methods. For realistic conditions, data-driven methods take the advantage of simple application. However, state-of-the-art machine learning (ML) algorithms are still kinds of black-box models; thus, the algorithms do not have a strong ability to describe the inner reactions or degradation information of batteries. Due to a lack of interpretability, machine learning may not learn the degradation principle correctly and may need to depend on big data quality. In this paper, we propose a physics-informed recurrent neural network (PIRNN) with a fractional-order gradient for fast battery degradation estimation in running EVs to provide a physics-informed neural network that can make algorithms learn battery degradation mechanisms. Incremental capacity analysis (ICA) was conducted to extract aging characteristics, which could be selected as the inputs of the algorithm. The fractional-order gradient descent (FOGD) method was also applied to improve the training convergence and embedding of battery information during backpropagation; then, the recurrent neural network was selected as the main body of the algorithm. A battery dataset with fast degradation from ten EVs with a total of 5697 charging snippets were constructed to validate the performance of the proposed algorithm. Experimental results show that the proposed PIRNN with ICA and the FOGD method could control the relative error within 5% for most snippets of the ten EVs. The algorithm could even achieve a stable estimation accuracy (relative error < 3%) during three-quarters of a battery’s lifetime, while for a battery with dramatic degradation, it was difficult to maintain such high accuracy during the whole battery lifetime. Full article
(This article belongs to the Special Issue Recent Advances in Fractional-Order Equations and Their Applications in Modern Energy Systems)
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16 pages, 2211 KiB  
Article
Distributed Consensus Fuzzy Control Method and Fractional Order Control for Power Sharing in Field Medical Microgrids under FDI Attacks
by Chenyu Wang, Wenyue Zhao, Lu Liu and Rui Wang
Fractal Fract. 2024, 8(10), 561; https://doi.org/10.3390/fractalfract8100561 - 27 Sep 2024
Viewed by 803
Abstract
Although field medical microgrids have been widely studied as an important component of future medical power systems, current sharing control in field medical microgrids under false information injection (FDI) attacks has rarely been researched. Based on this, this paper proposes a distributed fuzzy [...] Read more.
Although field medical microgrids have been widely studied as an important component of future medical power systems, current sharing control in field medical microgrids under false information injection (FDI) attacks has rarely been researched. Based on this, this paper proposes a distributed fuzzy control method for power sharing in field medical microgrids considering communication networks under FDI attacks. First, the field medical microgrid is modeled as a multi-bus DC microgrid system with power coupling. To provide voltage control and initial current equalization, fractional order PI control is applied. In order to reduce the model complexity, the concept of block modeling is employed to transform the model into a linear heterogeneous multi-agent system. Secondly, a fully distributed current sharing fuzzy control strategy is proposed. It can precisely realize current sharing control and reduce the communication bandwidth. Finally, the proposed control strategy is verified by simulation results. Full article
(This article belongs to the Special Issue Recent Advances in Fractional-Order Equations and Their Applications in Modern Energy Systems)
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