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Fractal Fract
Special Issues
Fractional Behavior in Nature
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Fractional Behavior in Nature

A special issue of Fractal and Fractional (ISSN 2504-3110).

Deadline for manuscript submissions: closed (31 October 2018) | Viewed by 5202

Special Issue Editor

Dr. Manuel Duarte Ortigueira

E-Mail Website
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
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

It is already known that the non-integer order systems can describe dynamical behavior of materials and processes over vast time and frequency scales, with very concise and computable models.

  1. There is evidence that most of the biological signals have spectra that do not increase or decrease by multiples of 20 dB/dec.
  2. The long-range processes (1/f noise sources)—the fractional Brownian motion (fBm) is the most famous—are very common in nature.
  3. The power law behaviour can be found in many peocesses.

On the other hand, and looking from a much deeper perspective, the fractional derivative implies causality. By respecting proper time order and including the effects of the past on the evolution of systems and processes, we open the door to a more realistic, non-Markovian, view of the world without drastically increasing the complexity of the system descriptions.

Prof. Dr. Manuel D. Ortigueira
Guest Editor

Keywords

  • fractional derivative
  • fractional integral
  • long range
  • power law
  • fractional models
  • fractional discrete-time systems
  • fractional continuous-time systems
  • ARFIMA

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Published Papers (1 paper)

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Research

13 pages, 1193 KiB  
Article
Fatigue-Induced Cole Electrical Impedance Model Changes of Biceps Tissue Bioimpedance
by Todd J. Freeborn and Bo Fu
Fractal Fract. 2018, 2(4), 27; https://doi.org/10.3390/fractalfract2040027 - 24 Oct 2018
Cited by 28 | Viewed by 4469
Abstract
Bioimpedance, or the electrical impedance of biological tissues, describes the passive electrical properties of these materials. To simplify bioimpedance datasets, fractional-order equivalent circuit presentations are often used, with the Cole-impedance model being one of the most widely used fractional-order circuits for this purpose. [...] Read more.
Bioimpedance, or the electrical impedance of biological tissues, describes the passive electrical properties of these materials. To simplify bioimpedance datasets, fractional-order equivalent circuit presentations are often used, with the Cole-impedance model being one of the most widely used fractional-order circuits for this purpose. In this work, bioimpedance measurements from 10 kHz to 100 kHz were collected from participants biceps tissues immediately prior and immediately post completion of a fatiguing exercise protocol. The Cole-impedance parameters that best fit these datasets were determined using numerical optimization procedures, with relative errors of within approximately ± 0.5 % and ± 2 % for the simulated resistance and reactance compared to the experimental data. Comparison between the pre and post fatigue Cole-impedance parameters shows that the R ∞ , R 1 , and f p components exhibited statistically significant mean differences as a result of the fatigue induced changes in the study participants. Full article
(This article belongs to the Special Issue Fractional Behavior in Nature)
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