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Symmetry
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Functional Analysis, Fractional Operators and Symmetry/Asymmetry: Second Edition
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Functional Analysis, Fractional Operators and Symmetry/Asymmetry: Second Edition

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

Deadline for manuscript submissions: closed (31 December 2024) | Viewed by 7604

Special Issue Editors

Dr. J. Vanterler Da C. Sousa

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Guest Editor
Department of Mathematics, Aerospace Engineering, PPGEA-UEMA, DEMATI-UEMA, São Luís 65054, Brazil
Interests: fractional differential equations; functional analysis; variational approach; frac-tional calculus; analysis mathematics
Special Issues, Collections and Topics in MDPI journals
Dr. Jiabin Zuo

E-Mail Website
Guest Editor
School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
Interests: fractional laplacian equations; partial differential equations
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Junesang Choi

E-Mail Website
Guest Editor
Department of Mathematics, Dongguk University, Wise Campus, Gyeongju 38066, Republic of Korea
Interests: special functions; analytic number theory; fractional calculus
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

It is a well-known fact that the role and effects of symmetry in mathematics and related sciences are of paramount importance. On many occasions, symmetries have been applied in mathematical formulations to solve complex problems, and thus, they have become essential and necessitate further research. Therefore, in this Special Issue, we aim to collate papers that underscore the theorical aspects and applications of symmetry in the fields of functional analysis and fractional operators.

Dr. J. Vanterler Da C. Sousa
Dr. Jiabin Zuo
Prof. Dr. Junesang Choi
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. 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

  • dynamical systems
  • partial differential equations
  • mathematical physics
  • symmetry operators
  • fractional operators
  • applied mathematics
  • discrete mathematics and graph theory
  • mathematical analysis
  • fractional differential equations
  • extension of linear operators
  • self-adjoint operators

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Published Papers (7 papers)

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Research

23 pages, 442 KiB  
Article
Dynamics of a Predator-Prey System with Asymmetric Dispersal and Fear Effect
by Xinyu Meng, Lijuan Chen and Fengde Chen
Symmetry 2025, 17(3), 329; https://doi.org/10.3390/sym17030329 - 22 Feb 2025
Cited by 1 | Viewed by 582
Abstract
Predator-prey interactions are among the most common and crucial ecological phenomena in nature. Over the course of long-term evolution, prey populations have developed various anti-predation strategies to cope with the threat of predators, with population dispersal being one of the most common strategies. [...] Read more.
Predator-prey interactions are among the most common and crucial ecological phenomena in nature. Over the course of long-term evolution, prey populations have developed various anti-predation strategies to cope with the threat of predators, with population dispersal being one of the most common strategies. In traditional ecological models, the prey population is typically constrained by direct predation. However, an increasing body of empirical evidence suggests that the fear effect from the predator significantly alters the physiological behavior of prey, leading to a decrease in reproduction rate and an increase in mortality rate. In this paper, we investigate a predator-prey system incorporating asymmetric dispersal and the fear effect, which influences the birth and death rates of the prey species. We rigorously establish the existence and local stability of equilibrium points, derive sufficient conditions for global stability, and prove the occurrence of a transcritical bifurcation at the boundary equilibrium. Our analysis reveals an optimal dispersal rate that maximizes prey population density; beyond this threshold, increased dispersal drives both populations to extinction. Furthermore, the fear effect and its maximum cost exhibit significant negative impacts on predator abundance, though they do not alter the equilibrium stability or existence. These findings provide critical insights for designing habitat corridors in endangered species conservation and underscore the pivotal role of prey dispersal in shaping population dynamics. Full article
(This article belongs to the Special Issue Functional Analysis, Fractional Operators and Symmetry/Asymmetry: Second Edition)
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14 pages, 272 KiB  
Article
The Space of Continuous Linear Functionals on ℓ1 Approximated by Weakly Symmetric Continuous Linear Functionals
by Taras Vasylyshyn and Andriy Zagorodnyuk
Symmetry 2025, 17(2), 206; https://doi.org/10.3390/sym17020206 - 29 Jan 2025
Viewed by 521
Abstract
We study the space of continuous linear functionals approximated by weakly symmetric continuous linear functionals on the complex Banach space ℓ1 of all absolutely summing complex sequences. We construct the sequence of groups of symmetries on ℓ1, obtain the structure [...] Read more.
We study the space of continuous linear functionals approximated by weakly symmetric continuous linear functionals on the complex Banach space ℓ1 of all absolutely summing complex sequences. We construct the sequence of groups of symmetries on ℓ1, obtain the structure of corresponding weakly symmetric continuous linear functionals, find the completion of the space, and construct for it a Schauder basis. Full article
(This article belongs to the Special Issue Functional Analysis, Fractional Operators and Symmetry/Asymmetry: Second Edition)
18 pages, 293 KiB  
Article
On Symmetrically Stochastic System of Fractional Differential Equations and Variational Inequalities
by Yue Zhang, Lu-Chuan Ceng, Jen-Chih Yao, Yue Zeng, Yun-Yi Huang and Si-Ying Li
Symmetry 2025, 17(1), 138; https://doi.org/10.3390/sym17010138 - 17 Jan 2025
Viewed by 721
Abstract
In this work, we are devoted to discussing a system of fractional stochastic differential variational inequalities with Lévy jumps (SFSDVI with Lévy jumps), that comprises both parts, that is, a system of stochastic variational inequalities (SSVI) and a system of fractional stochastic differential [...] Read more.
In this work, we are devoted to discussing a system of fractional stochastic differential variational inequalities with Lévy jumps (SFSDVI with Lévy jumps), that comprises both parts, that is, a system of stochastic variational inequalities (SSVI) and a system of fractional stochastic differential equations(SFSDE) with Lévy jumps. Here it is noteworthy that the SFSDVI with Lévy jumps consists of both sections that possess a mutual symmetry structure. Invoking Picard’s successive iteration process and projection technique, we obtain the existence of only a solution to the SFSDVI with Lévy jumps via some appropriate restrictions. In addition, the major outcomes are invoked to deduce that there is only a solution to the spatial-price equilibria system in stochastic circumstances. The main contributions of the article are listed as follows: (a) putting forward the SFSDVI with Lévy jumps that could be applied for handling different real matters arising from varied domains; (b) deriving the unique existence of solutions to the SFSDVI with Lévy jumps under a few mild assumptions; (c) providing an applicable instance for spatial-price equilibria system in stochastic circumstances affected with Lévy jumps and memory. Full article
(This article belongs to the Special Issue Functional Analysis, Fractional Operators and Symmetry/Asymmetry: Second Edition)
27 pages, 326 KiB  
Article
Parametrized Half-Hyperbolic Tangent Function-Activated Complex-Valued Neural Network Approximation
by George A. Anastassiou and Seda Karateke
Symmetry 2024, 16(12), 1568; https://doi.org/10.3390/sym16121568 - 23 Nov 2024
Cited by 1 | Viewed by 740
Abstract
In this paper, we create a family of neural network (NN) operators employing a parametrized and deformed half-hyperbolic tangent function as an activation function and a density function produced by the same activation function. Moreover, we consider the univariate quantitative approximations by complex-valued [...] Read more.
In this paper, we create a family of neural network (NN) operators employing a parametrized and deformed half-hyperbolic tangent function as an activation function and a density function produced by the same activation function. Moreover, we consider the univariate quantitative approximations by complex-valued neural network (NN) operators of complex-valued functions on a compact domain. Pointwise and uniform convergence results on Banach spaces are acquired through trigonometric, hyperbolic, and hybrid-type hyperbolic–trigonometric approaches. Full article
(This article belongs to the Special Issue Functional Analysis, Fractional Operators and Symmetry/Asymmetry: Second Edition)
21 pages, 293 KiB  
Article
Composition Operators on Weighted Zygmund Spaces of the First Loo-keng Hua Domain
by Hong-Bin Bai
Symmetry 2024, 16(7), 828; https://doi.org/10.3390/sym16070828 - 1 Jul 2024
Viewed by 1103
Abstract
Let HEI denote the first Loo-keng Hua domain. In this paper, we obtain many elementary results on HEI by the continuous and careful discussions. In some applications, we obtain some necessary conditions or sufficient conditions for the boundedness and compactness of [...] Read more.
Let HEI denote the first Loo-keng Hua domain. In this paper, we obtain many elementary results on HEI by the continuous and careful discussions. In some applications, we obtain some necessary conditions or sufficient conditions for the boundedness and compactness of the composition operators on weighted Zygmund space defined on HEI. Full article
(This article belongs to the Special Issue Functional Analysis, Fractional Operators and Symmetry/Asymmetry: Second Edition)
29 pages, 1484 KiB  
Article
On the Sums over Inverse Powers of Zeros of the Hurwitz Zeta Function and Some Related Properties of These Zeros
by Sergey Sekatskii
Symmetry 2024, 16(3), 326; https://doi.org/10.3390/sym16030326 - 7 Mar 2024
Viewed by 1160
Abstract
Recently, we have applied the generalized Littlewood theorem concerning contour integrals of the logarithm of the analytical function to find the sums over inverse powers of zeros for the incomplete gamma and Riemann zeta functions, polygamma functions, and elliptical functions. Here, the same [...] Read more.
Recently, we have applied the generalized Littlewood theorem concerning contour integrals of the logarithm of the analytical function to find the sums over inverse powers of zeros for the incomplete gamma and Riemann zeta functions, polygamma functions, and elliptical functions. Here, the same theorem is applied to study such sums for the zeros of the Hurwitz zeta function ζ(s,z), including the sum over the inverse first power of its appropriately defined non-trivial zeros. We also study some related properties of the Hurwitz zeta function zeros. In particular, we show that, for any natural N and small real ε, when z tends to n = 0, −1, −2… we can find at least N zeros of ζ(s,z) in the ε neighborhood of 0 for sufficiently small |z+n|, as well as one simple zero tending to 1, etc. Full article
(This article belongs to the Special Issue Functional Analysis, Fractional Operators and Symmetry/Asymmetry: Second Edition)
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25 pages, 897 KiB  
Article
Numerical Algorithms for Approximation of Fractional Integrals and Derivatives Based on Quintic Spline Interpolation
by Mariusz Ciesielski
Symmetry 2024, 16(2), 252; https://doi.org/10.3390/sym16020252 - 18 Feb 2024
Cited by 3 | Viewed by 1793
Abstract
Numerical algorithms for calculating the left- and right-sided Riemann–Liouville fractional integrals and the left- and right-sided fractional derivatives in the Caputo sense using spline interpolation techniques are derived. The spline of the fifth degree (the so-called quintic spline) is mainly taken into account, [...] Read more.
Numerical algorithms for calculating the left- and right-sided Riemann–Liouville fractional integrals and the left- and right-sided fractional derivatives in the Caputo sense using spline interpolation techniques are derived. The spline of the fifth degree (the so-called quintic spline) is mainly taken into account, but the linear and cubic splines are also considered to compare the quality of the developed method and numerical calculations. The estimation of errors for the derived approximation algorithms is presented. Examples of the numerical evaluation of the fractional integrals and derivatives are executed using 128-bit floating-point numbers and arithmetic routines. For each derived algorithm, the experimental orders of convergence are calculated. Also, an illustrative computational example showing the action of the considered fractional operators on the symmetric function in the interval is presented. Full article
(This article belongs to the Special Issue Functional Analysis, Fractional Operators and Symmetry/Asymmetry: Second Edition)
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