The Applications of Fractional Calculus in Control Engineering, Dynamical Systems and Signal Processing

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 31 December 2025 | Viewed by 1792

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División Académica de Mecánica Industrial, Universidad Tecnológica Emiliano Zapata, Emiliano Zapata, Morelos 62765, Mexico
Interests: control theory; fractional calculus; computational neuroscience; robotics and mechatronics
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Special Issue Information

Dear Colleagues,

I invite you to submit your recent and novel work in this Special Issue of Mathematics. Fractional-order calculus deals with derivatives and integrals in which the order is non-integer. There is an increasing interest in the study of fractional-order systems because fractional-order dynamics can model complex phenomena, which is not possible with integer-order dynamics. An important characteristic of fractional-order systems is the memory associated with the kernel of the derivative, which in most cases can be non-local, non-singular or both. Memory plays an important role in fractional-order systems because it allows us to model non-local behavior, and, in most cases, to predict future events in the systems. All these properties, among others, are allowing the development of new investigations in areas such as control engineering, dynamical systems, signal processing, and so on. This Special Issue will focus on such areas, but will not be limited to them. Therefore, I encourage the submission of novel investigations on the use of fractional-order dynamics, fractional-order control systems, signal processes, and any novel work related to fractional-order calculus. I am sure your important contributions will expand the state of the art in fractional-order systems.

Dr. Antonio Coronel-Escamilla
Guest Editor

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Keywords

  • fractional calculus
  • fractional-order control systems
  • fractional-order dynamics
  • signal processing
  • synchronization
  • memory trace

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Published Papers (1 paper)

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Research

13 pages, 1088 KiB  
Article
Generalized Kelvin–Voigt Creep Model in Fractal Space–Time
by Eduardo Reyes de Luna, Andriy Kryvko, Juan B. Pascual-Francisco, Ignacio Hernández and Didier Samayoa
Mathematics 2024, 12(19), 3099; https://doi.org/10.3390/math12193099 - 3 Oct 2024
Cited by 1 | Viewed by 1251
Abstract
In this paper, we study the creep phenomena for self-similar models of viscoelastic materials and derive a generalization of the Kelvin–Voigt model in the framework of fractal continuum calculus. Creep compliance for the Kelvin–Voigt model is extended to fractal manifolds through local fractal-continuum [...] Read more.
In this paper, we study the creep phenomena for self-similar models of viscoelastic materials and derive a generalization of the Kelvin–Voigt model in the framework of fractal continuum calculus. Creep compliance for the Kelvin–Voigt model is extended to fractal manifolds through local fractal-continuum differential operators. Generalized fractal creep compliance is obtained, taking into account the intrinsic time τ and the fractal dimension of time-scale β. The model obtained is validated with experimental data obtained for resin samples with the fractal structure of a Sierpinski carpet and experimental data on rock salt. Comparisons of the model predictions with the experimental data are presented as the curves of slow continuous deformations. Full article
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