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Fractal Fract
Special Issues
Complexity, Fractality and Fractional Dynamics Applied to Science and Engineering
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Complexity, Fractality and Fractional Dynamics Applied to Science and Engineering

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

Deadline for manuscript submissions: 31 October 2024 | Viewed by 7646

Special Issue Editors

Dr. Alexandra M.S.F. Galhano

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Guest Editor
Faculdade de Ciências Naturais, Engenharias e Tecnologias, Universidade Lusófona do Porto, Rua Augusto Rosa 24, 4000-098 Porto, Portugal
Interests: systems modelling; dynamics; multidimensional scaling; fractional calculus
Prof. Dr. Sergio Adriani David

E-Mail Website
Guest Editor
Faculdade de Zootecnia e Engenharia de Alimentos da USP, University of São Paulo, Av. Duque de Caxias-Norte, 225, Jardim Elite, Pirassununga 13635-900, SP, Brazil
Interests: fractional order systems; fractional behaviour; fractional modelling for time series; fractional modelling in econophysics; fractional modelling in biological systems; nonlinear phenomena; fractals and chaos
Special Issues, Collections and Topics in MDPI journals
Dr. António Lopes

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Guest Editor
Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200–465 Porto, Portugal
Interests: complex systems modelling; automation and robotics; fractional order systems modelling and control; data analysis and visualization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Many problems in classical and quantum physics, statistical physics, engineering, biology, psychology, economics, and finance are of a global nature (rather than simply local) and their behavior is often characterized by long-range correlations in the time–space domain, memory effects, fractality, and power law dynamics. The fractional calculus and fractional processes have been extensively adopted in various areas and have become one of the most useful approaches to deal with particular properties of non-locality and representation of (long) memory effects in a myriad of applied sciences. Indeed, the fractional paradigm applies not only to calculus but also to stochastic processes. Moreover, big data analysis, organization, retrieval, and modeling are important tools for a computational approach to address complex, fractal, and fractional dynamics.

This Special Issue (SI) is important, not only to present the state of the art for complex, fractal, and fractional dynamics and their applications, but also to reveal the potential and the extension of those tools to model real world phenomena. Original, rigorous, and high-quality contributions are welcome to this SI and should fit the scope of the journal. Potential authors should address topics that include, but are not limited to, the following:

  • Memory (univariate and multivariate) models;
  • Complex and fractional modeling for time series;
  • Complex and fractional modeling in econophysics;
  • Complex and fractional approaches in biosystems and biophysics;
  • Complex and fractional dynamics in oncology;
  • Mathematical psychology;
  • Fractals;
  • Fractal-Fractional order mathematical models;
  • Fractional non-linear dynamics and chaos;
  • Big data in complex and fractional dynamics;
  • Fractional order advanced control systems: cyber-physical systems, machine learning, robotics, mechanical systems, etc.

Dr. Alexandra M.S.F. Galhano
Prof. Dr. Sergio Adriani David
Dr. António Lopes
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.

Keywords

  • fractional-order systems
  • memory
  • econophysics
  • time series
  • finance
  • economics, big data
  • complex systems
  • biosystems
  • fractals

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Published Papers (5 papers)

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Research

19 pages, 1159 KiB  
Article
Formation of Optical Fractals by Chaotic Solitons in Coupled Nonlinear Helmholtz Equations
by M. Mossa Al-Sawalha, Saima Noor, Mohammad Alqudah, Musaad S. Aldhabani and Rasool Shah
Fractal Fract. 2024, 8(10), 594; https://doi.org/10.3390/fractalfract8100594 - 10 Oct 2024
Viewed by 408
Abstract
In the present research work, we construct and examine the self-similarity of optical solitons by employing the Riccati Modified Extended Simple Equation Method (RMESEM) within the framework of non-integrable Coupled Nonlinear Helmholtz Equations (CNHEs). This system models the transmission of optical solitons and [...] Read more.
In the present research work, we construct and examine the self-similarity of optical solitons by employing the Riccati Modified Extended Simple Equation Method (RMESEM) within the framework of non-integrable Coupled Nonlinear Helmholtz Equations (CNHEs). This system models the transmission of optical solitons and coupled wave packets in nonlinear optical fibers and describes transverse effects in nonlinear fiber optics. Initially, a complex transformation is used to convert the model into a single Nonlinear Ordinary Differential Equation (NODE), from which hyperbolic, exponential, rational, trigonometric, and rational hyperbolic solutions are produced. In order to better understand the physical dynamics, we offer several 3D, contour, and 2D illustrations for the independent selections of physical parameter values. These illustrations highlight the graphic behaviour of some optical solitons and demonstrate that, under certain constraint conditions, acquired optical solitons lose their stability when they approach an axis and display periodic-axial perturbations, which lead to the generation of optical fractals. As a framework, the generated optical solitons have several useful applications in the field of telecommunications. Furthermore, our suggested RMESEM demonstrates its use by broadening the spectrum of optical soliton solutions, offering important insights into the dynamics of the CNHEs, and suggesting possible applications in the management of nonlinear models. Full article
(This article belongs to the Special Issue Complexity, Fractality and Fractional Dynamics Applied to Science and Engineering)
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17 pages, 356 KiB  
Article
Information Properties of Consecutive Systems Using Fractional Generalized Cumulative Residual Entropy
by Mohamed Kayid and Mansour Shrahili
Fractal Fract. 2024, 8(10), 568; https://doi.org/10.3390/fractalfract8100568 - 28 Sep 2024
Viewed by 315
Abstract
We investigate some information properties of consecutive k-out-of-n:G systems in light of fractional generalized cumulative residual entropy. We firstly derive a formula to compute fractional generalized cumulative residual entropy related to the system’s lifetime and explore its preservation properties in [...] Read more.
We investigate some information properties of consecutive k-out-of-n:G systems in light of fractional generalized cumulative residual entropy. We firstly derive a formula to compute fractional generalized cumulative residual entropy related to the system’s lifetime and explore its preservation properties in terms of established stochastic orders. Additionally, we obtain useful bounds. To aid practical applications, we propose two nonparametric estimators for the fractional generalized cumulative residual entropy in these systems. The efficiency and performance of these estimators are illustrated using simulated and real datasets. Full article
(This article belongs to the Special Issue Complexity, Fractality and Fractional Dynamics Applied to Science and Engineering)
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12 pages, 1090 KiB  
Article
Dynamics of the Traveling Wave Solutions of Fractional Date–Jimbo–Kashiwara–Miwa Equation via Riccati–Bernoulli Sub-ODE Method through Bäcklund Transformation
by M. Mossa Al-Sawalha, Saima Noor, Mohammad Alqudah, Musaad S. Aldhabani and Roman Ullah
Fractal Fract. 2024, 8(9), 497; https://doi.org/10.3390/fractalfract8090497 - 23 Aug 2024
Viewed by 597
Abstract
The dynamical wave solutions of the time–space fractional Date–Jimbo–Kashiwara–Miwa (DJKM) equation have been obtained in this article using an innovative and efficient technique including the Riccati–Bernoulli sub-ODE method through Bäcklund transformation. Fractional-order derivatives enter into play for their novel contribution to the enhancement [...] Read more.
The dynamical wave solutions of the time–space fractional Date–Jimbo–Kashiwara–Miwa (DJKM) equation have been obtained in this article using an innovative and efficient technique including the Riccati–Bernoulli sub-ODE method through Bäcklund transformation. Fractional-order derivatives enter into play for their novel contribution to the enhancement of the characterization of dynamic waves while providing better modeling ability compared to integer types of derivatives. The solutions of the above-mentioned time–space fractional Date–Jimbo–Kashiwara–Miwa equation have tremendous importance in numerous scientific scenarios. The regular dynamical wave solutions of the aforementioned equation encompass three fundamental functions: trigonometric, hyperbolic, and rational functions will be among the topics covered. These solutions are graphically classified into three categories: compacton kink solitary wave solutions, kink soliton wave solutions and anti-kink soliton wave solutions. In addition, to explore the impact of the fractional parameter (α) on those solutions, 2D plots are utilized, while 3D plots are applied to present the solutions involving the integer-order derivatives. Full article
(This article belongs to the Special Issue Complexity, Fractality and Fractional Dynamics Applied to Science and Engineering)
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23 pages, 2057 KiB  
Article
Navigating Choppy Waters: Interplay between Financial Stress and Commodity Market Indices
by Haji Ahmed, Faheem Aslam and Paulo Ferreira
Fractal Fract. 2024, 8(2), 96; https://doi.org/10.3390/fractalfract8020096 - 4 Feb 2024
Viewed by 2034
Abstract
Financial stress can have significant implications for individuals, businesses, asset prices and the economy as a whole. This study examines the nonlinear structure and dynamic changes in the multifractal behavior of cross-correlation between the financial stress index (FSI) and four well-known commodity indices, [...] Read more.
Financial stress can have significant implications for individuals, businesses, asset prices and the economy as a whole. This study examines the nonlinear structure and dynamic changes in the multifractal behavior of cross-correlation between the financial stress index (FSI) and four well-known commodity indices, namely Commodity Research Bureau Index (CRBI), Baltic Dry Index (BDI), London Metal Index (LME) and Brent Oil prices (BROIL), using multifractal detrended cross correlation analysis (MFDCCA). For analysis, we utilized daily values of FSI and commodity index prices from 16 June 2016 to 9 July 2023. The following are the most important empirical findings: (I) All of the chosen commodity market indices show cross correlations with the FSI and have notable multifractal characteristics. (II) The presence of power law cross-correlation implies that a noteworthy shift in FSI is likely to coincide with a considerable shift in the commodity indices. (III) The multifractal cross-correlation is highest between FSI and Brent Oil (BROIL) and lowest with LME. (IV) The rolling windows analysis reveals a varying degree of persistency between FSI and commodity markets. The findings of this study have a number of important implications for commodity market investors and policymakers. Full article
(This article belongs to the Special Issue Complexity, Fractality and Fractional Dynamics Applied to Science and Engineering)
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43 pages, 16277 KiB  
Article
The Multiscale Principle in Nature (Principium luxuriæ): Linking Multiscale Thermodynamics to Living and Non-Living Complex Systems
by Patricio Venegas-Aravena and Enrique G. Cordaro
Fractal Fract. 2024, 8(1), 35; https://doi.org/10.3390/fractalfract8010035 - 4 Jan 2024
Cited by 3 | Viewed by 3374
Abstract
Why do fractals appear in so many domains of science? What is the physical principle that generates them? While it is true that fractals naturally appear in many physical systems, it has so far been impossible to derive them from first physical principles. [...] Read more.
Why do fractals appear in so many domains of science? What is the physical principle that generates them? While it is true that fractals naturally appear in many physical systems, it has so far been impossible to derive them from first physical principles. However, a proposed interpretation could shed light on the inherent principle behind the creation of fractals. This is the multiscale thermodynamic perspective, which states that an increase in external energy could initiate energy transport mechanisms that facilitate the dissipation or release of excess energy at different scales. Within this framework, it is revealed that power law patterns, and to a lesser extent, fractals, can emerge as a geometric manifestation to dissipate energy in response to external forces. In this context, the exponent of these power law patterns (thermodynamic fractal dimension D) serves as an indicator of the balance between entropy production at small and large scales. Thus, when a system is more efficient at releasing excess energy at the microscopic (macroscopic) level, D tends to increase (decrease). While this principle, known as Principium luxuriæ, may sound promising for describing both multiscale and complex systems, there is still uncertainty about its true applicability. Thus, this work explores different physical, astrophysical, sociological, and biological systems to attempt to describe and interpret them through the lens of the Principium luxuriæ. The analyzed physical systems correspond to emergent behaviors, chaos theory, and turbulence. To a lesser extent, the cosmic evolution of the universe and geomorphology are examined. Biological systems such as the geometry of human organs, aging, human brain development and cognition, moral evolution, Natural Selection, and biological death are also analyzed. It is found that these systems can be reinterpreted and described through the thermodynamic fractal dimension. Therefore, it is proposed that the physical principle that could be behind the creation of fractals is the Principium luxuriæ, which can be defined as “Systems that interact with each other can trigger responses at multiple scales as a manner to dissipate the excess energy that comes from this interaction”. That is why this framework has the potential to uncover new discoveries in various fields. For example, it is suggested that the reduction in D in the universe could generate emergent behavior and the proliferation of complexity in numerous fields or the reinterpretation of Natural Selection. Full article
(This article belongs to the Special Issue Complexity, Fractality and Fractional Dynamics Applied to Science and Engineering)
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