Special Issue "Symmetries and Fuzzy Differential Equations"

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

Deadline for manuscript submissions: 30 April 2024 | Viewed by 2373

Special Issue Editors

Department of Physics, Zhejiang Normal University, Jinhua 321004,China
Interests: general relativity; black holes; symmetries; wormhole; modified theories of gravity
Special Issues, Collections and Topics in MDPI journals
School of Physics and Electronic Information Engineering, Zhejiang Normal University, Jinhua 321004, China
Interests: differential equations; theoretical physics; applied mathematics; pure mathematics; biological systems; network engineering

Special Issue Information

Dear Colleagues,

Researchers have long been aware of the solutions and applications of differential equations due to the significant role that these equations play in physics, image processing, mechanics, viscoelasticity, hydrology, electromagnetics, fluid mechanics, and many other fields. In recent times, researchers have grown more eager to work on differential equations, including fractional order, concurrently with the development of mathematical methods and computer software. As a result, a variety of techniques are now employed to solve differential equations, such as different numerical methods. Differential equations are employed widely in gravity research. The approximation symmetry technique is critical in determining the exact solutions of differential equations. Some of the most powerful Lie group approaches, such as symmetries, symmetry groups, and symmetry reductions, have also been taken into consideration to solve differential equations. Fuzzy differential equations have recently gained significant interest in the scientific community, hence the creation of this Special Issue, for which

  • Differential equations;
  • Geometric nature of differential equations;
  • Probing fractional order differential equations ;
  • Fuzzy differential equations;
  • Symmetries;
  • Lie symmetries;
  • Applications of differential equations;
  • Discovery of differential equation solutions using conformal symmetries;
  • Differential equations in research on gravity;
  • Numerical solutions of differential equations;
  • Biological systems.

Dr. Ghulam Mustafa
Prof. Dr. Emmanuel Kengne
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.


  • differential equations
  • partial differential equations
  • system of differential equations
  • conformal symmetries
  • lie symmetries
  • noether symmetries
  • fluid mechanics
  • fuzzy differential equations
  • fractional order differential equations
  • fuzzy fractional order differential equations
  • numerical solutions
  • gravity researches
  • quantum mechanics
  • systems of differential equations
  • systems of partial differential equations
  • systems of fractional order differential equations
  • systems of fractional order partial differential equations
  • soliton theory

Published Papers (1 paper)

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25 pages, 816 KiB  
Extremal Solutions for Surface Energy Minimization: Bicubically Blended Coons Patches
Symmetry 2023, 15(6), 1237; https://doi.org/10.3390/sym15061237 - 09 Jun 2023
Viewed by 1661
A Coons patch is characterized by a finite set of boundary curves, which are dependent on the choice of blending functions. For a bicubically blended Coons patch (BBCP), the Hermite cubic polynomials (interpolants) are used as blending functions. A BBCP comprises information about [...] Read more.
A Coons patch is characterized by a finite set of boundary curves, which are dependent on the choice of blending functions. For a bicubically blended Coons patch (BBCP), the Hermite cubic polynomials (interpolants) are used as blending functions. A BBCP comprises information about its four corner points, including the curvature represented by eight tangent vectors, as well as the twisting behavior determined by the four twist vectors at these corner points. The interior shape of the BBCP depends not only on the tangent vectors at the corner points but on the twist vectors as well. The alteration in the twist vectors at the corner points can change the interior shape of the BBCP even for the same arrangement of tangent vectors at these corner points. In this study, we aim to determine the optimal twist vectors that would make the surface an extremal of the minimal energy functional. To achieve this, we obtain the constraints on the optimal twist vectors (MPDs) of the BBCP for the specified corner points by computing the extremal of the Dirichlet and quasi-harmonic functionals over the entire surface with respect to the twist vectors. These twist vectors can then be used to construct various quasi-minimal and quasi-harmonic BBCPs by varying corner points and tangent vectors. The optimization techniques involve minimizing a functional subject to certain constraints. The methods used to optimize twist vectors of BBCPs can have potential applications in various fields. They can be applied to fuzzy optimal control problems, allowing us to find the solution of complex and uncertain systems with fuzzy constraints. They provide us an opportunity to incorporate symmetry considerations for the partial differential equations associated with minimal surface equations, an outcome of zero-mean curvature for such surfaces. By exploring and utilizing the underlying symmetries, the optimization strategies can be further enhanced in terms of robustness and adaptability. Full article
(This article belongs to the Special Issue Symmetries and Fuzzy Differential Equations)
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