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Fractal Fract
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Fractional Processes and Systems in Computer Science and Engineering
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Fractional Processes and Systems in Computer Science and Engineering

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

Deadline for manuscript submissions: 30 November 2025 | Viewed by 4736

Special Issue Editors

Prof. Dr. Ming Li

E-Mail Website
Guest Editor
Ocean College, Zhejiang University, Hangzhou 310027, China
Interests: fractal time series; long-range dependent processes; self-similar processes; fractional derivative; fractional processes; fractional oscillation equation; fractional Brownian motion; fractional Gaussian noise and its applications; ships and ocean engineering; network traffic; computer science; mathematics; statistics; mechanics; systems sciences
Special Issues, Collections and Topics in MDPI journals
Dr. Junyu He

E-Mail Website
Guest Editor
Department of Marine Science, Ocean College, Zhejiang University, Zhoushan 316000, China
Interests: spatiotemporal data analysis; remote sensing; spatiotemporal geostatistics; artificial intelligence; blue carbon
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Fractional processes and systems are increasingly attracting the interest of researchers in various fields, ranging from computer science to geophysics. This Special Issue focuses on two aspects: One is the theory of fractional processes and systems. The other is the applications of fractional processes and systems in fields such as computer science, data communications, network security, solid mechanics, marine science, ecology, and so on.

The aim of this Special Issue is to develop the theory and applications of fractional processes and systems, including the application of fractional processes to computer networks and applications of fractional systems in engineering, such as fractional vibrations, fractional mechanics, applications of fractal dimensions to ecosystem research such as biodiversity identification, and so forth.

This Special Issue aims at collecting high-quality papers, including original research articles, perspectives, and reviews, covering recent advances in the areas of, but not limited to, the theory and applications of fractional processes and systems.

Prof. Dr. Ming Li
Dr. Junyu He
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 processes
  • fractional systems
  • fractal dimensions
  • fractal time series
  • long-range dependence
  • fractal paths
  • anomalous diffusion behavior
  • stochastic processes
  • fractional Brownian motion
  • fractional derivative
  • fractional Gaussian noise
  • fractional models

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

Published Papers (4 papers)

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22 pages, 17423 KiB  
Article
Theoretical Analysis of Viscoelastic Friction System Characteristics of Robotic Arm Brake Based on Fractional Differential Theory
by Wenli Ma, Qiaoling Du, Wenhao Li and Zhenqi Yang
Fractal Fract. 2024, 8(10), 565; https://doi.org/10.3390/fractalfract8100565 - 28 Sep 2024
Viewed by 439
Abstract
In engineering practice, the nonlinear vibration effect can easily lead to chaos in the system, which will not only reduce the performance of the system but also lead to premature fatigue of components, control failure, and increased safety risks. In view of the [...] Read more.
In engineering practice, the nonlinear vibration effect can easily lead to chaos in the system, which will not only reduce the performance of the system but also lead to premature fatigue of components, control failure, and increased safety risks. In view of the core position of the robotic arm in modern industry, this study relies on the robotic arm brake system to explore the theoretical basis of integrated viscoelastic materials as a vibration isolation layer. By analyzing the dynamic characteristics of the friction braking system with fractional differential terms, it aims to provide a new perspective for understanding and controlling the chaotic phenomena of a class of nonlinear friction systems. Firstly, we construct a model of a friction system and analyze its dynamic characteristics in detail. The self-excited vibration of the system under disturbance is studied. The relationship between amplitude and frequency is calculated by a nonlinear approximate analytical algorithm, and the accuracy of this relationship is verified by a numerical algorithm. Then, we compare the differences between non-fractional systems and fractional systems. It is found that with the increase in the fractional order term, the vibration amplitude of the system decreases significantly, which helps to reduce the nonlinear characteristics generated by the friction system and narrow the range of unstable solutions. Secondly, we also study the influence of parameter coefficients on the amplitude–frequency characteristics and analyze the local static bifurcation characteristics through singularity theory. Finally, we study the dynamic bifurcation behavior under different parameter perturbations and find that the change in system parameters will lead to the alternation of periodic motion and chaotic motion. Full article
(This article belongs to the Special Issue Fractional Processes and Systems in Computer Science and Engineering)
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20 pages, 2303 KiB  
Article
A Low-Computational Burden Closed-Form Approximated Expression for MSE Applicable for PTP with gfGn Environment
by Yehonatan Avraham and Monika Pinchas
Fractal Fract. 2024, 8(7), 418; https://doi.org/10.3390/fractalfract8070418 - 17 Jul 2024
Viewed by 634
Abstract
The Precision Time Protocol (PTP) plays a pivotal role in achieving precise frequency and time synchronization in computer networks. However, network delays and jitter in real systems introduce uncertainties that can compromise synchronization accuracy. Three clock skew estimators designed for the PTP scenario [...] Read more.
The Precision Time Protocol (PTP) plays a pivotal role in achieving precise frequency and time synchronization in computer networks. However, network delays and jitter in real systems introduce uncertainties that can compromise synchronization accuracy. Three clock skew estimators designed for the PTP scenario were obtained in our earlier work, complemented by closed-form approximations for the Mean Squared Error (MSE) under the generalized fractional Gaussian noise (gfGn) model, incorporating the Hurst exponent parameter (H) and the a parameter. These expressions offer crucial insights for network designers, aiding in the strategic selection and implementation of clock skew estimators. However, substantial computational resources are required to fit each expression to the gfGn model parameters (H and a) from the MSE perspective requirement. This paper introduces new closed-form estimates that approximate the MSE tailored to match gfGn scenarios that have a lower computational burden compared to the literature-known expressions and that are easily adaptable from the computational burden point of view to different pairs of H and a parameters. Thus, the system requires less substantial computational resources and might be more cost-effective. Full article
(This article belongs to the Special Issue Fractional Processes and Systems in Computer Science and Engineering)
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24 pages, 5127 KiB  
Article
Fractional Calculus to Analyze Efficiency Behavior in a Balancing Loop in a System Dynamics Environment
by Jorge Manuel Barrios-Sánchez, Roberto Baeza-Serrato and Leonardo Martínez-Jiménez
Fractal Fract. 2024, 8(4), 212; https://doi.org/10.3390/fractalfract8040212 - 4 Apr 2024
Viewed by 1298
Abstract
This research project focuses on developing a mathematical model that allows us to understand the behavior of the balancing loops in system dynamics in greater detail and precision. Currently, simulations give us an understanding of the behavior of these loops, but under the [...] Read more.
This research project focuses on developing a mathematical model that allows us to understand the behavior of the balancing loops in system dynamics in greater detail and precision. Currently, simulations give us an understanding of the behavior of these loops, but under the premise of an ideal scenario. In practice, however, accurate models often operate with varying efficiencies due to various irregularities and particularities. This discrepancy is the primary motivation behind our research proposal, which seeks to provide a more realistic understanding of the behavior of the loops, including their different levels of efficiency. To achieve this goal, we propose the introduction of fractional calculus in system dynamics models, focusing specifically on the balancing loops. This innovative approach offers a new perspective on the state of the art, offering new possibilities for understanding and optimizing complex systems. Full article
(This article belongs to the Special Issue Fractional Processes and Systems in Computer Science and Engineering)
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12 pages, 2733 KiB  
Article
Space–Time Variations in the Long-Range Dependence of Sea Surface Chlorophyll in the East China Sea and the South China Sea
by Junyu He and Ming Li
Fractal Fract. 2024, 8(2), 102; https://doi.org/10.3390/fractalfract8020102 - 7 Feb 2024
Cited by 1 | Viewed by 1504
Abstract
Gaining insights into the space–time variations in the long-range dependence of sea surface chlorophyll is crucial for the early detection of environmental issues in oceans. To this end, 12 locations were selected along the Yangtze River and Pearl River estuaries, varying in distances [...] Read more.
Gaining insights into the space–time variations in the long-range dependence of sea surface chlorophyll is crucial for the early detection of environmental issues in oceans. To this end, 12 locations were selected along the Yangtze River and Pearl River estuaries, varying in distances from the Chinese coastline. Daily satellite-observed sea surface chlorophyll concentration data at these 12 locations were collected from the Copernicus Marine Service website, spanning from December 1997 to November 2023. The main objective of the current study is to introduce a multi-fractional generalized Cauchy model for calculating the values of Hurst exponents and quantitatively assessing the long-range dependence strength of sea surface chlorophyll at different spatial locations and time instants during the study period. Furthermore, ANOVA was utilized to detect the differences of calculated Hurst exponent values among the locations during various months and seasons. From a spatial perspective, the findings reveal a significantly stronger long-range dependence of sea surface chlorophyll in offshore regions compared to nearshore areas, with Hurst exponent values > 0.5 versus <0.5. It is noteworthy that the values of Hurst exponents at each location exhibit significant differences during various seasons, from a temporal perspective. Specifically, the long-range dependence of sea surface chlorophyll in summer in the nearshore region is weaker than in other seasons, whereas that in the offshore region is stronger than in other seasons. The study concludes that long-range dependence is inversely related to the distance from the coastline, and anthropogenic activity plays a dominant role in shaping the long-range dependence of sea surface chlorophyll in the coastal regions of China. Full article
(This article belongs to the Special Issue Fractional Processes and Systems in Computer Science and Engineering)
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