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 4248

Special Issue Editors


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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

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

Published Papers (3 papers)

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Research

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 1 | Viewed by 1354
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
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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
Viewed by 825
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
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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 1264
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
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