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Symmetry
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Discussion of Properties and Applications of Integral Transform
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Discussion of Properties and Applications of Integral Transform

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

Deadline for manuscript submissions: 30 September 2025 | Viewed by 5656

Special Issue Editor

Prof. Dr. Hwajoon Kim

E-Mail Website
Guest Editor
Department of IT Engineering, Kyungdong University, Yangju 11458, Republic of Korea
Interests: mathematics; integral transform; integral equation; measure theory; math in deep learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Integral transform is an old theory, but it has application value enough to be applied to CT or MRI technology. When a solution cannot be found in a certain space, or it is difficult to find the solution, we can think of another space. After finding the solution in this other space, you can find the solution in the original space by using inverse transform. This principle forms the center of integral transform theory.

The topics we would like to focus on are as follows, but other topics are also welcome.

  • Radon transform;
  • Wavelet and Curvelet transforms;
  • Generalized integral transforms;
  • Fourier transform and its applications;
  • Application in AI;
  • Hypercomplex generalization of integral transforms;
  • Kernel theory;
  • Application in Engineering;
  • Convolution theory;
  • Integral Equations etc.

Prof. Dr. Hwajoon Kim
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

  • radon transform
  • wavelet and curvelet transforms
  • generalized integral transforms
  • Fourier transform and its applications
  • application in AI
  • hypercomplex generalization of integral transforms
  • kernel theory
  • application in engineering
  • convolution theory
  • integral equations

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Published Papers (5 papers)

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Research

13 pages, 266 KiB  
Article
Some Estimates for Certain q-analogs of Gamma Integral Transform Operators
by Shrideh Al-Omari, Wael Salameh and Sharifah Alhazmi
Symmetry 2024, 16(10), 1368; https://doi.org/10.3390/sym16101368 - 15 Oct 2024
Viewed by 1118
Abstract
The aim of this work is to examine some q-analogs and differential properties of the gamma integral operator and its convolution products. The q-gamma integral operator is introduced in two versions in order to derive pertinent conclusions regarding the q-exponential [...] Read more.
The aim of this work is to examine some q-analogs and differential properties of the gamma integral operator and its convolution products. The q-gamma integral operator is introduced in two versions in order to derive pertinent conclusions regarding the q-exponential functions. Also, new findings on the q-trigonometric, q-sine, and q-cosine functions are extracted. In addition, novel results for first and second-order q-differential operators are established and extended to Heaviside unit step functions. Lastly, three crucial convolution products and extensive convolution theorems for the q-analogs are also provided. Full article
(This article belongs to the Special Issue Discussion of Properties and Applications of Integral Transform)
12 pages, 264 KiB  
Article
Notes on q-Gamma Operators and Their Extension to Classes of Generalized Distributions
by Shrideh Al-Omari, Wael Salameh and Sharifah Alhazmi
Symmetry 2024, 16(10), 1294; https://doi.org/10.3390/sym16101294 - 2 Oct 2024
Viewed by 756
Abstract
This paper discusses definitions and properties of q-analogues of the gamma integral operator and its extension to classes of generalized distributions. It introduces q-convolution products, symmetric q-delta sequences and q-quotients of sequences, and establishes certain convolution theorems. The convolution [...] Read more.
This paper discusses definitions and properties of q-analogues of the gamma integral operator and its extension to classes of generalized distributions. It introduces q-convolution products, symmetric q-delta sequences and q-quotients of sequences, and establishes certain convolution theorems. The convolution theorems are utilized to accomplish q-equivalence classes of generalized distributions called q-Boehmians. Consequently, the q-gamma operators are therefore extended to the generalized spaces and performed to coincide with the classical integral operator. Further, the generalized q-gamma integral is shown to be linear, sequentially continuous and continuous with respect to some involved convergence equipped with the generalized spaces. Full article
(This article belongs to the Special Issue Discussion of Properties and Applications of Integral Transform)
17 pages, 329 KiB  
Article
On Some Formulas for Single and Double Integral Transforms Related to the Group SO(2, 2)
by I. A. Shilin and Junesang Choi
Symmetry 2024, 16(9), 1102; https://doi.org/10.3390/sym16091102 - 23 Aug 2024
Viewed by 1046
Abstract
We present a novel proof, using group theory, for a Meijer transform formula. This proof reveals the formula as a specific case of a broader generalized result. The generalization is achieved through a linear operator that intertwines two representations of the connected component [...] Read more.
We present a novel proof, using group theory, for a Meijer transform formula. This proof reveals the formula as a specific case of a broader generalized result. The generalization is achieved through a linear operator that intertwines two representations of the connected component of the identity of the group SO(2,2). Using this same approach, we derive a formula for the sum of three double integral transforms, where the kernels are represented by Bessel functions. It is particularly noteworthy that the group SO(2,2) is connected to symmetry in several significant ways, especially in mathematical physics and geometry. Full article
(This article belongs to the Special Issue Discussion of Properties and Applications of Integral Transform)
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28 pages, 339 KiB  
Article
Application of the Triple Laplace Transform Decomposition Method for Solving Singular (2 + 1)-Dimensional Time-Fractional Coupled Korteweg–De Vries Equations (KdV)
by Hassan Eltayeb Gadain, Imed Bachar and Said Mesloub
Symmetry 2024, 16(8), 1055; https://doi.org/10.3390/sym16081055 - 15 Aug 2024
Viewed by 988
Abstract
The main aim of this article is to modify the space-time fractionalKdV equations using the Bessel operator. The triple Laplace transform decomposition method (TLTDM) is proposed to find the solution for a time-fractional singular KdV coupled system of equations. Three problems are discussed [...] Read more.
The main aim of this article is to modify the space-time fractionalKdV equations using the Bessel operator. The triple Laplace transform decomposition method (TLTDM) is proposed to find the solution for a time-fractional singular KdV coupled system of equations. Three problems are discussed to check the accuracy and illustrate the effectiveness of this technique. The results imply that our method is very active and easy to utilize while analyzing the manner of nonlinear fractional differential equations appearing in the joint field of science and mathematics. Moreover, this method is fast convergent if we compare it with the existing techniques in the literature. Full article
(This article belongs to the Special Issue Discussion of Properties and Applications of Integral Transform)
17 pages, 297 KiB  
Article
A Note on the Application of the Double Sumudu–Generalized Laplace Decomposition Method and 1+1- and 2+1-Dimensional Time-Fractional Boussinesq Equations
by Hassan Eltayeb and Said Mesloub
Symmetry 2024, 16(6), 665; https://doi.org/10.3390/sym16060665 - 28 May 2024
Viewed by 749
Abstract
The current paper concentrates on discovering the exact solutions of the singular time-fractional Boussinesq equation and coupled time-fractional Boussinesq equation by presenting a new technique known as the double Sumudu–generalized Laplace and Adomian decomposition method. Here, two main theorems are addressed that are [...] Read more.
The current paper concentrates on discovering the exact solutions of the singular time-fractional Boussinesq equation and coupled time-fractional Boussinesq equation by presenting a new technique known as the double Sumudu–generalized Laplace and Adomian decomposition method. Here, two main theorems are addressed that are very useful in this work. Moreover, the mentioned method is effective in solving several problems. Some examples are presented to check the precision and symmetry of the technique. The outcomes show that the proposed technique is precise and gives better solutions as compared to existing methods in the literature. Full article
(This article belongs to the Special Issue Discussion of Properties and Applications of Integral Transform)
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