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Symmetry
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Symmetry in Functional Equations: Methods, Applications and Mathematical Models
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Symmetry in Functional Equations: Methods, Applications and Mathematical Models

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 6258

Special Issue Editors

Dr. Alexandra Galhano

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Guest Editor
Faculdade de Ciências Naturais, Engenharias e Tecnologias, Universidade Lusófona do Porto, R. de Augusto Rosa 24, 4000-098 Porto, Portugal
Interests: systems modelling; dynamics; multidimensional scaling; fractional calculus
Special Issues, Collections and Topics in MDPI journals
Dr. Omid Nikan

E-Mail Website
Guest Editor
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran
Interests: numerical analysis; fractional differential equations; differential equations; meshless methods; numerical methods
Special Issues, Collections and Topics in MDPI journals
Dr. Zakieh Avazzadeh

E-Mail Website
Guest Editor
Department of Applied Mathematics, Xi'an Jiaotong-Liverpool University, Suzhou 215123, China
Interests: fractional calculus; PDE; optimal control; nonlinear dynamics; numerical approximation method
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Functional equations have a long and interesting history in connection with mathematical physics and touch upon many branches of mathematics. They have arisen in the context of both classical and quantum models, being completely integrable systems in several different ways. The aim of this Special Issue is to assemble innovative papers on the theory, methodology, and applications of symmetric/asymmetric mathematical models and methods, applied to various areas of science. We encourage submissions presenting original works with high scientific merit on statistical, computational, and mathematical approaches with an emphasis on behavioral science, biology, biomedical sciences, computer science, data analytics, economics and management, engineering, epidemiology, genomics and genetics, and medicine and social sciences.

Dr. Alexandra Galhano
Dr. Omid Nikan
Dr. Zakieh Avazzadeh
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

  • mathematical modelling
  • numerical methods
  • random differential equations
  • optimization problems
  • engineering applications

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (4 papers)

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Research

21 pages, 353 KiB  
Article
On Solutions of Some Functional Equations of Radical Type
by Janusz Brzdęk
Symmetry 2024, 16(11), 1517; https://doi.org/10.3390/sym16111517 - 12 Nov 2024
Viewed by 473
Abstract
Many authors have studied various functional equations of forms patterned on the equation expressed as ga2+b2=g(a)+g(b), which can be considered, e.g., for real functions. Such equations are [...] Read more.
Many authors have studied various functional equations of forms patterned on the equation expressed as ga2+b2=g(a)+g(b), which can be considered, e.g., for real functions. Such equations are usually referred to as radical functional equations or of the radical type. Authors mainly study the so-called Ulam stability of such equations, i.e., they investigate how much the mappings satisfying the equations approximately (in a sense) differ from the exact solutions of these equations. Quite often, information about the solutions of these equations is also provided, but unfortunately, sometimes, such information is given in a misleading or incomplete way. It seems, therefore, that there is a need for a publication containing simple descriptions of such solutions (with appropriate examples), which would help in easy correction of such information and avoidance of similar problems for future authors. This is the main motivation for this expository paper. We present a general approach to the topic and consider two general forms of such equations. Moreover, the results presented in this paper show significant symmetry between the solutions of numerous functional equations and the solutions of equations of the radical type that correspond to them. To make this publication accessible to a wider audience, we omit various related information, avoid advanced generalizations, and present several simple examples. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations: Methods, Applications and Mathematical Models)
10 pages, 16122 KiB  
Article
Solving Fractional Order Differential Equations by Using Fractional Radial Basis Function Neural Network
by Rana Javadi, Hamid Mesgarani, Omid Nikan and Zakieh Avazzadeh
Symmetry 2023, 15(6), 1275; https://doi.org/10.3390/sym15061275 - 17 Jun 2023
Cited by 4 | Viewed by 1912
Abstract
Fractional differential equations (FDEs) arising in engineering and other sciences describe nature sufficiently in terms of symmetry properties. This paper proposes a numerical technique to approximate ordinary fractional initial value problems by applying fractional radial basis function neural network. The fractional derivative used [...] Read more.
Fractional differential equations (FDEs) arising in engineering and other sciences describe nature sufficiently in terms of symmetry properties. This paper proposes a numerical technique to approximate ordinary fractional initial value problems by applying fractional radial basis function neural network. The fractional derivative used in the method is considered Riemann-Liouville type. This method is simple to implement and approximates the solution of any arbitrary point inside or outside the domain after training the ANN model. Finally, three examples are presented to show the validity and applicability of the method. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations: Methods, Applications and Mathematical Models)
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10 pages, 1348 KiB  
Article
Numerical Approximation of a Time-Fractional Modified Equal-Width Wave Model by Using the B-Spline Weighted Residual Method
by Akeel A. AL-saedi and Jalil Rashidinia
Symmetry 2023, 15(4), 891; https://doi.org/10.3390/sym15040891 - 10 Apr 2023
Cited by 1 | Viewed by 1184
Abstract
Fractional calculus (FC) is an important mathematical tool in modeling many dynamical processes. Therefore, some analytical and numerical methods have been proposed, namely, those based on symmetry and spline schemes. This paper proposed a numerical approach for finding the solution to the time-fractional [...] Read more.
Fractional calculus (FC) is an important mathematical tool in modeling many dynamical processes. Therefore, some analytical and numerical methods have been proposed, namely, those based on symmetry and spline schemes. This paper proposed a numerical approach for finding the solution to the time-fractional modified equal-width wave (TFMEW) equation. The fractional derivative is described in the Caputo sense. Indeed, the B-spline Galerkin scheme combined with functions with different weights was employed to discretize TFMEW. The L2 and L∞ error norm values and the three invariants I1, I2, and I3 of the numerical example were calculated and tabulated. A comparison of these errors and invariants was provided to confirm the efficiency and accuracy of the proposed method. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations: Methods, Applications and Mathematical Models)
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12 pages, 297 KiB  
Article
Solving a System of Integral Equations in Rectangular Menger Probabilistic Metric Spaces and Rectangular Menger Probabilistic b-Metric Spaces
by Ehsan Lotfali Ghasab, Reza Chaharpashlou and António M. Lopes
Symmetry 2023, 15(1), 70; https://doi.org/10.3390/sym15010070 - 27 Dec 2022
Cited by 2 | Viewed by 1586
Abstract
This work introduces the concepts of rectangular Menger probabilistic metric (RMPM) space and rectangular Menger probabilistic b-metric (RMPbM) space as generalizations of the Menger probabilistic metric space and the Menger probabilistic [...] Read more.
This work introduces the concepts of rectangular Menger probabilistic metric (RMPM) space and rectangular Menger probabilistic b-metric (RMPbM) space as generalizations of the Menger probabilistic metric space and the Menger probabilistic b-metric space, respectively. Some nonunique fixed-point and coupled-fixed-point results for contractive mappings are provided. The findings extend and improve outcomes presented in the existing literature. The main results are illustrated with examples, and validated by means of an application to a system of integral equations. The importance of spaces with non-Hausdorff topology is high, as is the case of computer science, with the Tarskian approach to programming language semantics. Full article
(This article belongs to the Special Issue Symmetry in Functional Equations: Methods, Applications and Mathematical Models)
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