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Symmetry
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New Trends on the Mathematical Models and Solitons Arising in...
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New Trends on the Mathematical Models and Solitons Arising in Real-World Problems, 2nd Edition

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 7909

Special Issue Editor

Prof. Dr. Haci Mehmet Baskonus

E-Mail Website
Guest Editor
Department of Mathematics, Faculty of Education, Harran University, Sanliurfa 63100, Turkey
Interests: partial differential equations; fractional calculus; analytical methods; numerical methods; mathematical physics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues, 

The essence of mathematical tools for exemplifying the practical problems that exist in daily life is as old as the world itself. Mathematical models in science and technology have recently attracted an increased amount of research attention with the aim of understanding, describing, and predicting the future behavior of natural phenomena. Recent studies on fractional calculus have been particularly popular among researchers due to their favorable properties when analyzing real-world models associated with properties such as anomalous diffusion, non-Markovian processes, random walk, long range, and, most importantly, heterogeneous behaviors. The concept of local differential operators, along with power-law settings and non-local differential operators, was suggested in order to accurately replicate the above-cited natural processes. The complexities of nature have led mathematicians and physicists to derive the most sophisticated and scientific mathematical operators to accurately replicate and capture pragmatic realities.

Mathematical physics plays a vital role in the study of the determinants and distribution of solitons. With the help of this, we can identify wave distributions in many fields of nonlinear sciences, and many experts have recently focused their work on this field. Further, these types of studies may help us to provide the foundation for developing public policy and make regulatory decisions relating to engineering problems, as well as to evaluate both existing and new perspectives. Major areas of mathematical physics studies with mathematical models include physics, symmetry, transmission, outbreak investigation, and epidemiological problems.

This particular issue is devoted to the collection of new results, extending from theory to practice, with the aim of developing new technological tools. This Special Issue will be focused on, but not limited to:

Topics:

  • Theoretical, computational, and experimental nature of mathematical physics models;
  • Review performance of mathematical models with fractional differential and integral equations;
  • Evaluation of models with different types of fractional operators;
  • Validation of models with fractal–fractional differential and integral operators;
  • Review of effect of new fractal differential and integral operators for modeling, such as epidemiological diseases, mathematical physics, soliton theory, and so on.

Prof. Dr. Haci Mehmet Baskonus
Guest Editor

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. Symmetry 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 2400 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

  • mathematical physics
  • partial differential equations
  • epidemic models
  • basic reproduction number
  • fractional differential equations
  • dynamical systems
  • stability analysis
  • bifurcation
  • optimal control

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Related Special Issue

Published Papers (8 papers)

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Research

12 pages, 2095 KiB  
Article
Phase Portraits and Abundant Soliton Solutions of a Hirota Equation with Higher-Order Dispersion
by Fengxia Wu, Nauman Raza, Younes Chahlaoui, Asma Rashid Butt and Haci Mehmet Baskonus
Symmetry 2024, 16(11), 1554; https://doi.org/10.3390/sym16111554 - 20 Nov 2024
Viewed by 318
Abstract
The Hirota equation, an advanced variant of the nonlinear Schrödinger equation with cubic nonlinearity, incorporates time-delay adjustments and higher-order dispersion terms, offering an enhanced approximation for wave propagation in optical fibers and oceanic systems. By utilizing the traveling wave transformation generated from Lie [...] Read more.
The Hirota equation, an advanced variant of the nonlinear Schrödinger equation with cubic nonlinearity, incorporates time-delay adjustments and higher-order dispersion terms, offering an enhanced approximation for wave propagation in optical fibers and oceanic systems. By utilizing the traveling wave transformation generated from Lie point symmetry analysis with the combination of generalized exponential differential rational function and modified Bernoulli sub-ODE techniques, several traveling wave solutions, such as periodic, singular-periodic, and kink solitons, emerge. To examine the solutions visually, parametric values are adjusted to create 3D, contour, and 2D illustrations. Additionally, the dynamic properties of the model are explored through bifurcation analysis. The exact results demonstrate that both techniques are practical and robust. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems, 2nd Edition)
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18 pages, 4020 KiB  
Article
A Conjugate Linearly Polarized Light Wave Along an Optical Fiber with the Berry Phase Model and Its Magnetic Trajectories According to the Conjugate Frame
by Muhammed Talat Sariaydin
Symmetry 2024, 16(11), 1518; https://doi.org/10.3390/sym16111518 - 13 Nov 2024
Viewed by 607
Abstract
In this article, we study how a linear polarized wave that is going along an optical fiber works, which is known not only as a curve on a Lie group but also as a rotation of the polarization plane. What we are trying [...] Read more.
In this article, we study how a linear polarized wave that is going along an optical fiber works, which is known not only as a curve on a Lie group but also as a rotation of the polarization plane. What we are trying to show in this article is that linear polarized light waves (PLWs) are related to the Berry phase. Moreover, we give magnetic curves created by N traveling in the electromagnetic trajectories and the optical fiber generated by the electric field N of the PLW moving through the optical fiber. With this described method, we present a mathematical model to conveniently generate the relationships between an optical fiber and the optical angular momentum in a three-dimensional Lie group. The conjugate frame we used in this article removes unnecessary bending around the tangent and enables a more dynamic characterization, which can still be applied even when the second derivative of the curve is zero. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems, 2nd Edition)
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16 pages, 9804 KiB  
Article
Fractional-Order Mathematical Modeling of Methicillin- Resistant Staphylococcus aureus Transmission in Hospitals
by Zuhur Alqahtani, Mohammed Shqair, Randa Albdaiwi and Ahmed Hagag
Symmetry 2024, 16(11), 1454; https://doi.org/10.3390/sym16111454 - 2 Nov 2024
Viewed by 513
Abstract
This article investigates the environmental contamination and antibiotic exposure effect on the transmission dynamics of the Methicillin-Resistant Staphylococcus aureus (MRSA) model in hospitals using the fractional Adams–Bashforth–Moulton Method (ABMM). This epidemic model simulates the dynamics of patient populations, bacterial contamination, and healthcare worker [...] Read more.
This article investigates the environmental contamination and antibiotic exposure effect on the transmission dynamics of the Methicillin-Resistant Staphylococcus aureus (MRSA) model in hospitals using the fractional Adams–Bashforth–Moulton Method (ABMM). This epidemic model simulates the dynamics of patient populations, bacterial contamination, and healthcare worker safety under varying conditions. This model provides critical insights into the interactions between hospital practices, environmental factors, and infection dynamics, demonstrating the importance of symmetry in balancing hospital admission and discharge rates to manage infection spread effectively. The analysis extends to the impact of environmental bacterial density and hospital admission rates on patient colonization. Increasing admission rates introduce more susceptible patients, exacerbating infection spread when bacterial density is high. Conversely, lower admission rates and bacterial density result in a more controlled infection environment. The model further investigates how varying discharge rates influence colonization dynamics, highlighting that effective discharge practices can mitigate infection spread, especially in high-bacterial density scenarios. It must be noted that this model is studied fractionally for the first time. Overall, this model provides critical insights into the interactions between hospital practices, environmental factors, and infection dynamics, offering valuable guidance for infection control strategies and hospital policy formulation. By adjusting fractional order constant (σ) values and analyzing different scenarios, this research aids in understanding and managing bacterial infections in healthcare settings. The proposed method is able to provide the results presented in the figures within this study considering the influence of many factors. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems, 2nd Edition)
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26 pages, 361 KiB  
Article
Solutions of Second-Order Nonlinear Implicit ψ-Conformable Fractional Integro-Differential Equations with Nonlocal Fractional Integral Boundary Conditions in Banach Algebra
by Yahia Awad and Yousuf Alkhezi
Symmetry 2024, 16(9), 1097; https://doi.org/10.3390/sym16091097 - 23 Aug 2024
Cited by 1 | Viewed by 556
Abstract
In this paper, we introduce and thoroughly examine new generalized ψ-conformable fractional integral and derivative operators associated with the auxiliary function ψ(t). We rigorously analyze and confirm the essential properties of these operators, including their semigroup behavior, linearity, [...] Read more.
In this paper, we introduce and thoroughly examine new generalized ψ-conformable fractional integral and derivative operators associated with the auxiliary function ψ(t). We rigorously analyze and confirm the essential properties of these operators, including their semigroup behavior, linearity, boundedness, and specific symmetry characteristics, particularly their invariance under time reversal. These operators not only encompass the well-established Riemann–Liouville and Hadamard operators but also extend their applicability. Our primary focus is on addressing complex fractional boundary value problems, specifically second-order nonlinear implicit ψ-conformable fractional integro-differential equations with nonlocal fractional integral boundary conditions within Banach algebra. We assess the effectiveness of these operators in solving such problems and investigate the existence, uniqueness, and Ulam–Hyers stability of their solutions. A numerical example is presented to demonstrate the theoretical advancements and practical implications of our approach. Through this work, we aim to contribute to the development of fractional calculus methodologies and their applications. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems, 2nd Edition)
15 pages, 453 KiB  
Article
Numerical Analysis of the Transfer Dynamics of Heavy Metals from Soil to Plant and Application to Contamination of Honey
by Atanas Atanasov, Slavi Georgiev and Lubin Vulkov
Symmetry 2024, 16(1), 110; https://doi.org/10.3390/sym16010110 - 18 Jan 2024
Cited by 1 | Viewed by 1043
Abstract
We analyze a mathematical model of the effects of soil contamination by heavy metals, which is expressed as systems of nonlinear ordinary differential equations (ODEs). The model is based on the symmetry dynamics of heavy metals soil–plant interactions. We aim to study this [...] Read more.
We analyze a mathematical model of the effects of soil contamination by heavy metals, which is expressed as systems of nonlinear ordinary differential equations (ODEs). The model is based on the symmetry dynamics of heavy metals soil–plant interactions. We aim to study this symmetric process and its long-term behavior, as well as to discuss the role of two crucial parameters, namely the flux of the hydrogen protons to the soil in rainfall events W(t), and the available water for roots p(t). We study the boundedness and positivity of the solution. Further, a parameter identification analysis of the model is presented. Numerical experiments with synthetic and realistic data of honeybee population are discussed. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems, 2nd Edition)
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19 pages, 3145 KiB  
Article
Design, Implementation and Comparative Analysis of Three Models for Estimation of Solar Radiation Components on a Horizontal Surface
by Ilyas Rougab, Oscar Barambones, Mohammed Yousri Silaa and Ali Cheknane
Symmetry 2024, 16(1), 71; https://doi.org/10.3390/sym16010071 - 5 Jan 2024
Cited by 1 | Viewed by 1385
Abstract
Solar radiation data play a pivotal role in harnessing solar energy. Unfortunately, the availability of these data is limited due to the sparse distribution of meteorological stations worldwide. This paper introduces and simulates three models designed for estimating and predicting global solar radiation [...] Read more.
Solar radiation data play a pivotal role in harnessing solar energy. Unfortunately, the availability of these data is limited due to the sparse distribution of meteorological stations worldwide. This paper introduces and simulates three models designed for estimating and predicting global solar radiation at ground level. Furthermore, it conducts an in-depth analysis and comparison of the simulation results derived from these models, utilizing measured data from selected sites in Algeria where such information is accessible. The focus of our study revolves around three empirical models: Capderou, Lacis and Hansen, and Liu and Jordan. These models utilize day number and solar factor as input parameters, along with the primary site’s geographical coordinates—longitude, latitude, and altitude. Additionally, meteorological parameters such as relative humidity, temperature, and pressure are incorporated into the models. The objective is to estimate global solar radiation for any given day throughout the year at the specified location. Upon simulation, the results highlight that the Capderou model exhibits superior accuracy in approximating solar components, demonstrating negligible deviations between real and estimated values, especially under clear-sky conditions. However, these models exhibit certain limitations in adverse weather conditions. Consequently, alternative approaches, such as fuzzy logic methods or models based on satellite imagery, become essential for accurate predictions in inclement weather scenarios. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems, 2nd Edition)
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18 pages, 1069 KiB  
Article
Inverse Problem Numerical Analysis of Forager Bee Losses in Spatial Environment without Contamination
by Atanas Z. Atanasov, Miglena N. Koleva and Lubin G. Vulkov
Symmetry 2023, 15(12), 2099; https://doi.org/10.3390/sym15122099 - 22 Nov 2023
Cited by 1 | Viewed by 1087
Abstract
We consider an inverse problem of recovering the mortality rate in the honey bee difference equation model, that tracks a forage honeybee leaving and entering the hive each day. We concentrate our analysis to the model without pesticide contamination in the symmetric spatial [...] Read more.
We consider an inverse problem of recovering the mortality rate in the honey bee difference equation model, that tracks a forage honeybee leaving and entering the hive each day. We concentrate our analysis to the model without pesticide contamination in the symmetric spatial environment. Thus, the mathematical problem is formulated as a symmetric inverse problem for reaction coefficient at final time constraint. We use the overspecified information to transform the inverse coefficient problem to the forward problem with non-local terms in the differential operator and the initial condition. First, we apply semidiscretization in space to the new nonsymmetric differential operator. Then, the resulting non-local nonsymmetric system of ordinary differential equations (ODEs) is discretized by three iterative numerical schemes using different time stepping. Results of numerical experiments which compare the efficiency of the numerical schemes are discussed. Results from numerical tests with synthetic and real data are presented and discussed, as well. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems, 2nd Edition)
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23 pages, 618 KiB  
Article
A Minimal Parameterization of Rigid Body Displacement and Motion Using a Higher-Order Cayley Map by Dual Quaternions
by Daniel Condurache and Ionuț Popa
Symmetry 2023, 15(11), 2011; https://doi.org/10.3390/sym15112011 - 1 Nov 2023
Cited by 1 | Viewed by 1207
Abstract
The rigid body displacement mathematical model is a Lie group of the special Euclidean group SE (3). This article is about the Lie algebra se (3) group. The standard exponential map from se (3) onto SE (3) is a natural parameterization of these [...] Read more.
The rigid body displacement mathematical model is a Lie group of the special Euclidean group SE (3). This article is about the Lie algebra se (3) group. The standard exponential map from se (3) onto SE (3) is a natural parameterization of these displacements. In technical applications, a crucial problem is the vector minimal parameterization of manifold SE (3). This paper presents a unitary variant of a general class of such vector parameterizations. In recent years, dual algebra has become a comprehensive framework for analyzing and computing the characteristics of rigid-body movements and displacements. Based on higher-order fractional Cayley transforms for dual quaternions, higher-order Rodrigues dual vectors and multiple vectorial parameters (extended by rotational cases) were computed. For the rigid body movement description, a dual tangent operator (for any vectorial minimal parameterization) was computed. This paper presents a unitary method for the initial value problem of the dual kinematic equation. Full article
(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems, 2nd Edition)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Computational models of neurodevelopmental symmetry-breaking
Authors: Roman Bauer
Affiliation: Department of Computer Science, University of Surrey, UK
Abstract: Computational modelling of biological symmetry-breaking processes allows to formulate and compare experimentally verifiable hypotheses, as well as gain fundamental insights. In particular, neural development comprises many such symmetry-breaking phenomena which often remain poorly understood. Hence, a number of studies have produced explainable computational models that capture various symmetry-breaking processes shaping brain architecture and function. Here, I review a diverse array of computational approaches that have been used to capture intricate dynamics governing neuronal pattern formation based on cellular differentiation, neuronal arborization and the formation of synaptic connectivity. Through a comprehensive analysis of the associated models, I highlight the role of key self-organization features that drive neural asymmetry. In addition, I highlight the importance of computational modelling in addressing the challenges posed by the complexity of experimental data, and consequential value for bridging the gab between experimental observations and conceptual understanding. Overall, by surveying the interdisciplinary landscape of computational modelling in this field, a comprehensive overview is drawn of the contributions made, the pertinent challenges and the opportunities that lie ahead in unravelling the intricacies of symmetry-breaking during neural development.

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