Continuous/Discrete-Time Fractional Systems: Modelling, Design and Estimation

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

Deadline for manuscript submissions: 20 December 2024 | Viewed by 3386

Special Issue Editors


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Guest Editor
Academia de Matemática, Universidad Autónoma de la Ciudad de México, Ciudad de México 09790, Mexico
Interests: operational calculus; fractional calculus; fractional systems

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Guest Editor
Centre of Technology and Systems-UNINOVA, NOVA School of Science and Technology, NOVA University of Lisbon, Quinta da Torre, 2829-516 Caparica, Portugal
Interests: signal processing; fractional signals and systems; EEG and ECG processing
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Special Issue Information

Dear Colleagues,

In the last thirty years, Fractional Calculus has become an integral part all scientific fields. Although not all the formulations are suitable for being used in applications, there are several tools that constitute true generalizations of classic operators and are suitable for describing real phenomena. In fact, many systems can be classified as either shift-invariant or scale-invariant and have fractional characteristics either in time or in frequency/scale. This means that some of the known fractional operators, namely those described by ARMA-type equations, are very useful in many areas, such as: diffusion, viscoelasticity, fluid mechanics, bioengineering, dynamics of mechanical, electronic and biological systems, signal processing, control, economy, and others.

The focus of this Special Issue is to continue to advance research on topics such as modelling, design and estimation relating to fractional order systems. Manuscripts addressing novel theoretical issues, as well as those on more specific applications, are welcome.

Potential topics include but are not limited to the following:
    • Fractional order systems modelling and identification
    • Shift-invariant fractional ARMA linear systems, continuous-time, and discrete-time.
    • System analysis and design
    • Scale invariant systems
    • Fractional differential or difference equations
    • Mathematical and numerical methods with emphasis on fractional order systems
    • Fractional Gaussian noise, fractional Brownian motion, and other stochastic processes
    • Applications

Prof. Dr. Gabriel Bengochea
Dr. Manuel Duarte Ortigueira
Guest Editors

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Keywords

  • autoregressive-moving average (ARMA)
  • shift-invariant
  • scale-invariant
  • fBm
  • Liouville
  • Liouville–Caputo
  • Hadamard
  • Riemann–Liouville
  • Dzherbashian–Caputo
  • Grunwald–Letnikov
  • two-sided Riesz–Feller derivatives

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Published Papers (2 papers)

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Research

21 pages, 586 KiB  
Article
An Operational Approach to Fractional Scale-Invariant Linear Systems
by Gabriel Bengochea and Manuel Duarte Ortigueira
Fractal Fract. 2023, 7(7), 524; https://doi.org/10.3390/fractalfract7070524 - 2 Jul 2023
Cited by 1 | Viewed by 998
Abstract
The fractional scale-invariant systems are introduced and studied, using an operational formalism. It is shown that the impulse and step responses of such systems belong to the vector space generated by some special functions here introduced. For these functions, the fractional scale derivative [...] Read more.
The fractional scale-invariant systems are introduced and studied, using an operational formalism. It is shown that the impulse and step responses of such systems belong to the vector space generated by some special functions here introduced. For these functions, the fractional scale derivative is a decremental index operator, allowing the construction of an algebraic framework that enables to compute the impulse and step responses of such systems. The effectiveness and accuracy of the method are demonstrated through various numerical simulations. Full article
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32 pages, 450 KiB  
Article
Discrete-Time Fractional Difference Calculus: Origins, Evolutions, and New Formalisms
by Manuel Duarte Ortigueira
Fractal Fract. 2023, 7(7), 502; https://doi.org/10.3390/fractalfract7070502 - 25 Jun 2023
Cited by 3 | Viewed by 1237
Abstract
Differences are introduced as outputs of linear systems called differencers, being considered two classes: shift and scale-invariant. Several types are presented, namely: nabla and delta, bilateral, tempered, bilinear, stretching, and shrinking. Both continuous and discrete-time differences are described. ARMA-type systems based on differencers [...] Read more.
Differences are introduced as outputs of linear systems called differencers, being considered two classes: shift and scale-invariant. Several types are presented, namely: nabla and delta, bilateral, tempered, bilinear, stretching, and shrinking. Both continuous and discrete-time differences are described. ARMA-type systems based on differencers are introduced and exemplified. In passing, the incorrectness of the usual delta difference is shown. Full article
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