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Fractal Fract
Special Issues
Fractional Order Modeling in Interdisciplinary Applications
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Fractional Order Modeling in Interdisciplinary Applications

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

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 5012

Special Issue Editors

Dr. Simona Coman

E-Mail Website
Guest Editor
Automation and Information Technology Department, Electrical Engineering and Computer Science Faculty, Transilvania University of Brasov, 500036 Brasov, Romania
Interests: fractional-order control; model reference adaptive systems; robust systems; systems theory; biological and electrical systems
Dr. Cristian Boldisor

E-Mail Website
Guest Editor
Automation and Information Technology Department, Electrical Engineering and Computer Science Faculty, Transilvania University of Brasov, 500036 Brasov, Romania
Interests: fuzzy and neural control; systems theory; biological and electrical systems

Special Issue Information

Dear Colleagues,

Nowadays, fractional calculus is used in many interdisciplinary applications due to its capability to assure superior modeling and the control of dynamical systems, with applications in biology, robotics, systems identification, electrical systems, traffic management, genetic systems and many other domains. Many researchers are attempting to describe the physical behavior of some complex or nonlinear processes using fractional-order differential equations, since they could transpose complex high-order dynamics in a compact and precise mathematical model. In system theory and control engineering, the concept of a fractional-order controller (FOC), with a noninteger order of derivatives and integrals, is gaining increasingly more attention from researchers. Many recent studies have pointed out that the FOCs can provide a faster response and better control performances.

The aim of this Special Issue is to gather recent theoretical studies, simulation experiments and practical implementations in modeling complex processes from various domains and in designing controllers using fractional-order calculus. Topics invited for submission include (but are not limited to):

  • The identification and modeling of fractional-order models;
  • The application of fractional-order control strategy for any type of dynamical systems;
  • Fractional-order systems analysis;
  • Time and frequency domains analysis of fractional-order models;
  • Fuzzy fractional-order PID control theory and applications;
  • Fractional-order models in biology and biomedical applications;
  • Fractional-order models and control in robotics;
  • Fractional-order control in classical control engineering applications.

Dr. Simona Coman
Dr. Cristian Boldisor
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 models
  • biological systems
  • electrical systems
  • fractional-order controllers
  • fractional-order identification
  • model reference adaptive control
  • traffic systems
  • robotic systems
  • fractional-order nonlinear systems
  • robust systems
  • fractional order in state-space theory
  • automotive systems
  • MIMO systems
  • fractional order in digital control
  • servo systems
  • fuzzy fractional order

Published Papers (3 papers)

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Research

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23 pages, 10311 KiB  
Article
Mathematical Modeling of COVID-19 with Vaccination Using Fractional Derivative: A Case Study
by Tian-Chuan Sun, Mahmoud H. DarAssi, Wafa F. Alfwzan, Muhammad Altaf Khan, Abdulaziz Saad Alqahtani, Saeed S. Alshahrani and Taseer Muhammad
Fractal Fract. 2023, 7(3), 234; https://doi.org/10.3390/fractalfract7030234 - 06 Mar 2023
Cited by 7 | Viewed by 1690
Abstract
Vaccination against any infectious disease is considered to be an effective way of controlling it. This paper studies a fractional order model with vaccine efficacy and waning immunity. We present the model’s dynamics under vaccine efficacy, the impact of immunization, and the waning [...] Read more.
Vaccination against any infectious disease is considered to be an effective way of controlling it. This paper studies a fractional order model with vaccine efficacy and waning immunity. We present the model’s dynamics under vaccine efficacy, the impact of immunization, and the waning of the vaccine on coronavirus infection disease. We analyze the model under their equilibrium points. The model under the equilibrium points is discussed and proven that it is locally asymptotically stable if Rv is lesser than unity. We present the backward bifurcation hypothesis of the model and show that there is a parameter β2 that causes the backward bifurcation in the imperfect vaccine model. We show certain assumptions when ψ=1 for the imperfect vaccine case; the model is both stable globally asymptotically at the disease-free (R0≤1) and endemic cases (R0>1). By using infected cases from the recent wave throughout Pakistan, we shall estimate the model parameters and calculate the numerical value of the basic reproductive number R0≈1.2591. We present the comprehensive graphical results for the realistic parameter values and show many useful suggestions regarding the elimination of the infection from society. The vaccination efficacy that provides an important role in disease elimination is discussed in detail. Full article
(This article belongs to the Special Issue Fractional Order Modeling in Interdisciplinary Applications)
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22 pages, 13031 KiB  
Article
Fractional-Order Gas Film Model
by Xu Tang, Ying Luo and Bin Han
Fractal Fract. 2022, 6(10), 561; https://doi.org/10.3390/fractalfract6100561 - 03 Oct 2022
Viewed by 1743
Abstract
In this paper, a fractional-order model of the gas film is proposed for the dynamic characteristics of an air bearing. Based on the dynamic characteristics common between gas film and viscoelastic body, the idea of the fractional-order equivalent modeling of the dynamic characteristics [...] Read more.
In this paper, a fractional-order model of the gas film is proposed for the dynamic characteristics of an air bearing. Based on the dynamic characteristics common between gas film and viscoelastic body, the idea of the fractional-order equivalent modeling of the dynamic characteristics of the gas film is presented to improve the modeling accuracy. Four fractional-order gas film (FOGF) models are introduced based on generalization of traditional viscoelastic models. The analysis of the characteristics of the FOGF models shows that the FOGF model can capture more complex dynamic characteristics and fit the real dynamic data of the gas film better than traditional models. A genetic algorithm particle swarm optimization (GA-PSO) method is used for parameter identification of the proposed models. The experimental results tested on the air bearing motion platform show that the FOGF models are superior in accuracy to the traditional equivalent models for the gas film. In particular, the fractional-order Maxwell gas film (FOMGF) model has the best capture accuracy compared to the other FOGF models and traditional models. Full article
(This article belongs to the Special Issue Fractional Order Modeling in Interdisciplinary Applications)
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Other

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12 pages, 446 KiB  
Brief Report
Nonexistence of Finite-Time Stable Equilibria in a Class of Nonlinear Integral Equations
by Aldo Jonathan Muñoz-Vázquez, Oscar Martinez-Fuentes and Guillermo Fernández-Anaya
Fractal Fract. 2023, 7(4), 320; https://doi.org/10.3390/fractalfract7040320 - 08 Apr 2023
Viewed by 1083
Abstract
This brief report studies conditions to ensure the nonexistence of finite-time stable equilibria in a class of systems that are described by means of nonlinear integral equations, whose kernels are part of some Sonine kernel pairs. It is firstly demonstrated that, under certain [...] Read more.
This brief report studies conditions to ensure the nonexistence of finite-time stable equilibria in a class of systems that are described by means of nonlinear integral equations, whose kernels are part of some Sonine kernel pairs. It is firstly demonstrated that, under certain criteria, a real-valued function that converges in finite-time to a constant value, different from the initial condition, and remains there afterwards, cannot have a Sonine derivative that also remains at zero after some finite time. Then, the concept of equilibrium is generalized to the case of equivalent equilibrium, and it is demonstrated that a nonlinear integral equation, whose kernel is part of some Sonine kernel pair, cannot possess equivalent finite-time stable equilibria. Finally, illustrative examples are presented. Full article
(This article belongs to the Special Issue Fractional Order Modeling in Interdisciplinary Applications)
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