$fractalfract-logo$

Submit to Fractal Fract Review for Fractal Fract Propose a Special Issue

Journal Menu

Journal Browser

► Journal Browser

Fractional Behavior in Nature 2021

Special Issue Editors
Special Issue Information
Published Papers

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

Deadline for manuscript submissions: closed (20 October 2021) | Viewed by 13623

Share This Special Issue

Special Issue Editors

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

Dr. Duarte Valério

E-Mail Website
Guest Editor

Instituto de Engenharia Mecânica (IDMEC), Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
Interests: fractional calculus; fractional control; wave energy conversion; data mining
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 the dynamical behavior of materials and processes over vast time and frequency scales, with very concise and computable models.

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

On the other hand, and looking from a much deeper perspective, the fractional derivative may imply causality. By respecting the 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 system descriptions.

Prof. Dr. Manuel Ortigueira
Prof. Dr. Duarte Valério
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.

Published Papers (6 papers)

Download All Papers

Order results

Result details

Show export options Show export options

Select all

Export citation of selected articles as:

Research

21 pages, 6562 KiB

Open AccessArticle

Cardiovascular Circulatory System and Left Carotid Model: A Fractional Approach to Disease Modeling

by José Emilio Traver, Cristina Nuevo-Gallardo, Inés Tejado, Javier Fernández-Portales, Juan Francisco Ortega-Morán, J. Blas Pagador and Blas M. Vinagre

Fractal Fract. 2022, 6(2), 64; https://doi.org/10.3390/fractalfract6020064 - 26 Jan 2022

Cited by 9 | Viewed by 2792

Abstract

Cardiovascular diseases (CVDs) remain the leading cause of death worldwide, according to recent reports from the World Health Organization (WHO). This fact encourages research into the cardiovascular system (CVS) from multiple and different points of view than those given by the medical perspective, highlighting among them the computational and mathematical models that involve experiments much simpler and less expensive to be performed in comparison with in vivo or in vitro heart experiments. However, the CVS is a complex system that needs multidisciplinary knowledge to describe its dynamic models, which help to predict cardiovascular events in patients with heart failure, myocardial or valvular heart disease, so it remains an active area of research. Firstly, this paper presents a novel electrical model of the CVS that extends the classic Windkessel models to the left common carotid artery motivated by the need to have a more complete model from a medical point of view for validation purposes, as well as to describe other cardiovascular phenomena in this area, such as atherosclerosis, one of the main risk factors for CVDs. The model is validated by clinical indices and experimental data obtained from clinical trials performed on a pig. Secondly, as a first step, the goodness of a fractional-order behavior of this model is discussed to characterize different heart diseases through pressure–volume (PV) loops. Unlike other models, it allows us to modify not only the topology, parameters or number of model elements, but also the dynamic by tuning a single parameter, the characteristic differentiation order; consequently, it is expected to provide a valuable insight into this complex system and to support the development of clinical decision systems for CVDs. Full article

(This article belongs to the Special Issue Fractional Behavior in Nature 2021)

► Show Figures

Figure 1

25 pages, 5232 KiB

Open AccessArticle

Fractal Methods and Power Spectral Density as Means to Explore EEG Patterns in Patients Undertaking Mental Tasks

by Carlos Alberto Valentim, Claudio Marcio Cassela Inacio, Jr. and Sergio Adriani David

Fractal Fract. 2021, 5(4), 225; https://doi.org/10.3390/fractalfract5040225 - 17 Nov 2021

Cited by 10 | Viewed by 2445

Abstract

Brain electrical activity recorded as electroencephalogram data provides relevant information that can contribute to a better understanding of pathologies and human behaviour. This study explores extant electroencephalogram (EEG) signals in search of patterns that could differentiate subjects undertaking mental tasks and reveals insights on said data. We estimated the power spectral density of the signals and found that the subjects showed stronger gamma brain waves during activity while presenting alpha waves at rest. We also found that subjects who performed better in those tasks seemed to present less power density in high-frequency ranges, which could imply decreased brain activity during tasks. In a time-domain analysis, we used Hall–Wood and Robust–Genton estimators along with the Hurst exponent by means of a detrented fluctuation analysis and found that the first two fractal measures are capable of better differentiating signals between the rest and activity datasets. The statistical results indicated that the brain region corresponding to Fp channels might be more suitable for analysing EEG data from patients conducting arithmetic tasks. In summary, both frequency- and time-based methods employed in the study provided useful insights and should be preferably used together in EEG analysis. Full article

(This article belongs to the Special Issue Fractional Behavior in Nature 2021)

► Show Figures

Figure 1

17 pages, 2038 KiB

Open AccessArticle

Estimating Conditional Power for Sequential Monitoring of Covariate Adaptive Randomized Designs: The Fractional Brownian Motion Approach

by Yiping Yang, Hongjian Zhu and Dejian Lai

Fractal Fract. 2021, 5(3), 114; https://doi.org/10.3390/fractalfract5030114 - 08 Sep 2021

Cited by 3 | Viewed by 1585

Abstract

Conditional power based on classical Brownian motion (BM) has been widely used in sequential monitoring of clinical trials, including those with the covariate adaptive randomization design (CAR). Due to some uncontrollable factors, the sequential test statistics under CAR procedures may not satisfy the independent increment property of BM. We confirm the invalidation of BM when the error terms in the linear model with CAR design are not independent and identically distributed. To incorporate the possible correlation structure of the increment of the test statistic, we utilize the fractional Brownian motion (FBM). We conducted a comparative study of the conditional power under BM and FBM. It was found that the conditional power under FBM assumption was mostly higher than that under BM assumption when the Hurst exponent was greater than 0.5. Full article

(This article belongs to the Special Issue Fractional Behavior in Nature 2021)

► Show Figures

Figure 1

13 pages, 3029 KiB

Open AccessArticle

Fractional Differential Equation-Based Instantaneous Frequency Estimation for Signal Reconstruction

by Bilgi Görkem Yazgaç and Mürvet Kırcı

Fractal Fract. 2021, 5(3), 83; https://doi.org/10.3390/fractalfract5030083 - 30 Jul 2021

Cited by 6 | Viewed by 1665

Abstract

In this paper, we propose a fractional differential equation (FDE)-based approach for the estimation of instantaneous frequencies for windowed signals as a part of signal reconstruction. This approach is based on modeling bandpass filter results around the peaks of a windowed signal as fractional differential equations and linking differ-integrator parameters, thereby determining the long-range dependence on estimated instantaneous frequencies. We investigated the performance of the proposed approach with two evaluation measures and compared it to a benchmark noniterative signal reconstruction method (SPSI). The comparison was provided with different overlap parameters to investigate the performance of the proposed model concerning resolution. An additional comparison was provided by applying the proposed method and benchmark method outputs to iterative signal reconstruction algorithms. The proposed FDE method received better evaluation results in high resolution for the noniterative case and comparable results with SPSI with an increasing iteration number of iterative methods, regardless of the overlap parameter. Full article

(This article belongs to the Special Issue Fractional Behavior in Nature 2021)

► Show Figures

Figure 1

11 pages, 886 KiB

Open AccessArticle

Adsorption on Fractal Surfaces: A Non Linear Modeling Approach of a Fractional Behavior

by Vincent Tartaglione, Jocelyn Sabatier and Christophe Farges

Fractal Fract. 2021, 5(3), 65; https://doi.org/10.3390/fractalfract5030065 - 10 Jul 2021

Cited by 4 | Viewed by 2129

Abstract

This article deals with the random sequential adsorption (RSA) of 2D disks of the same size on fractal surfaces with a Hausdorff dimension

1 < d < 2

. According to the literature and confirmed by numerical simulations in the paper, the high [...] Read more.

This article deals with the random sequential adsorption (RSA) of 2D disks of the same size on fractal surfaces with a Hausdorff dimension

1 < d < 2

. According to the literature and confirmed by numerical simulations in the paper, the high coverage regime exhibits fractional dynamics, i.e., dynamics in

t^{- 1 / d}

where d is the fractal dimension of the surface. The main contribution this paper is that it proposes to capture this behavior with a particular class of nonlinear model: a driftless control affine model. Full article

(This article belongs to the Special Issue Fractional Behavior in Nature 2021)

► Show Figures

Figure 1

10 pages, 786 KiB

Open AccessArticle

Solutions of Bernoulli Equations in the Fractional Setting

by Mirko D’Ovidio, Anna Chiara Lai and Paola Loreti

Fractal Fract. 2021, 5(2), 57; https://doi.org/10.3390/fractalfract5020057 - 17 Jun 2021

Cited by 3 | Viewed by 1888

Abstract

We present a general series representation formula for the local solution of the Bernoulli equation with Caputo fractional derivatives. We then focus on a generalization of the fractional logistic equation and present some related numerical simulations. Full article

(This article belongs to the Special Issue Fractional Behavior in Nature 2021)

► Show Figures

Journal Menu

Journal Browser

Fractional Behavior in Nature 2021

Share This Special Issue

Special Issue Editors

Special Issue Information

Published Papers (6 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI