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Axioms
Special Issues
Fractional Calculus: From Fundamentals to Modern Applications
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Fractional Calculus: From Fundamentals to Modern Applications

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 1890

Special Issue Editor

Prof. Dr. Marcelo Kaminski Lenzi

E-Mail Website1 Website2
Guest Editor
Departamento de Engenharia Química, Universidade Federal do Paraná, Curitiba 81531-990, PR, Brazil
Interests: fractional calculus; process control; diffusion phenomena
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Since 1695, fractional calculus has been used extensively in fundamental and applied research. The primary goal of this Special Issue is to provide readers with state-of-the-art research publications that will not only serve as an updated literature review and knowledge update, but also as a means of providing ideas and challenges for future research, and perhaps a platform for different research groups around the world to collaborate in the future. Therefore, manuscripts with fundamental research involving mathematical methods, novel derivative definitions, and numerical methods for faster solutions, among others, are very welcome. Furthermore, applied research studies will definitely aid in the development of an insightful Special Issue by examining fractional calculus applications to different research fields. These fields include process system engineering, transport phenomena, biological systems, electrical circuits, and materials science. By taking these two branches, fundamental and applied research, into account, this Special Issue acts as a valuable reference for both beginners and senior researchers. It is relevant to see how far we can push knowledge and scientific boundaries by employing fractional calculus, and you are invited to contribute to this journey!

Prof. Dr. Marcelo Kaminski Lenzi
Guest Editor

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. Axioms 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 2400 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

  • mathematical methods
  • numerical methods
  • process systems engineering
  • biological systems
  • transport phenomena
  • material science

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Published Papers (1 paper)

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Research

19 pages, 3847 KiB  
Article
A Novel Fractional Multi-Order High-Gain Observer Design to Estimate Temperature in a Heat Exchange Process
by Vicente Borja-Jaimes, Manuel Adam-Medina, Jarniel García-Morales, Alan Cruz-Rojas, Alfredo Gil-Velasco and Antonio Coronel-Escamilla
Axioms 2023, 12(12), 1107; https://doi.org/10.3390/axioms12121107 - 8 Dec 2023
Cited by 2 | Viewed by 1506
Abstract
In the present manuscript, we design a fractional multi-order high-gain observer to estimate temperature in a double pipe heat exchange process. For comparison purposes and since we want to prove that when using our novel technique, the estimation is more robust than the [...] Read more.
In the present manuscript, we design a fractional multi-order high-gain observer to estimate temperature in a double pipe heat exchange process. For comparison purposes and since we want to prove that when using our novel technique, the estimation is more robust than the classical approach, we design a non-fractional high-gain observer, and then we compare the performance of both observers. We consider three scenarios: The first one considers the estimation of the system states by measuring only one output with no noise added on it and under ideal conditions. Second, we add noise to the measured output and then reconstruct the system states, and, third, in addition to the noise, we increase the gain parameter in both observers (non-fractional and fractional) due to the fact that we want to prove that the robustness changes in this parameter. The results showed that, using our approach, the estimated states can be recovered under noise circumstances in the measured output and under parameter change in the observer, contrary to using classical (non-fractional) observers where the states cannot be recovered. In all our tests, we used the normalized root-mean-square, integral square error, and integral absolute error indices, resulting in a better performance for our approach than that obtained using the classical approach. We concluded that our fractional multi-order high-gain observer is more robust to input noise than the classical high-gain observer. Full article
(This article belongs to the Special Issue Fractional Calculus: From Fundamentals to Modern Applications)
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