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Symmetry
Special Issues
Integral Transformation, Operational Calculus and Their Applications III
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Integral Transformation, Operational Calculus and Their Applications III

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

Deadline for manuscript submissions: 30 April 2025 | Viewed by 3851

Special Issue Editor

Prof. Dr. Hari Mohan Srivastava

grade E-Mail Website
Guest Editor
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Interests: real and complex analysis; fractional calculus and its applications; integral equations and transforms; higher transcendental functions and their applications; q-series and q-polynomials; analytic number theory; analytic and geometric Inequalities; probability and statistics; inventory modeling and optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The theory and applications of integral transformations and associated operational calculus are remarkably widespread in many diverse areas of the mathematical, physical, chemical, engineering, and statistical sciences. In this Special Issue, we invite and welcome review, expository, and original research articles dealing with the recent advances on the topics of integral transformations and operational calculus as well as their multidisciplinary applications involving their symmetry properties and characteristics.

Prof. Dr. Hari Mohan Srivastava
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

  • integral transformations and integral equations as well as other related operators including their symmetry properties and characteristics
  • applications involving mathematical (or higher transcendental) functions including their symmetry properties and characteristics
  • applications involving fractional-order differential and differintegral equations and their associated symmetry
  • applications involving symmetrical aspect of geometric function theory of complex analysis
  • applications involving q-series and q-polynomials and their associated symmetry
  • applications involving special functions of mathematical physics and applied mathematics and their symmetrical aspect
  • applications involving analytic number theory and symmetry

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

Published Papers (3 papers)

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Research

21 pages, 604 KiB  
Article
New Results on Differential Subordination and Superordination for Multivalent Functions Involving New Symmetric Operator
by Abdul Rahman S. Juma, Nihad Hameed Shehab, Daniel Breaz, Luminiţa-Ioana Cotîrlă, Maslina Darus and Alin Danciu
Symmetry 2024, 16(10), 1326; https://doi.org/10.3390/sym16101326 - 8 Oct 2024
Viewed by 407
Abstract
This article aims to significantly advance geometric function theory by providing a valuable contribution to analytic and multivalent functions. It focuses on differential subordination and superordination, which characterize the interactions between analytic functions. To achieve our goal, we employ a method that relies [...] Read more.
This article aims to significantly advance geometric function theory by providing a valuable contribution to analytic and multivalent functions. It focuses on differential subordination and superordination, which characterize the interactions between analytic functions. To achieve our goal, we employ a method that relies on the characteristics of differential subordination and superordination. As one of the latest advancements in this field, this technique is able to derive several results about differential subordination and superordination for multivalent functions defined by the new operator Mλ,pmv,ρ;ηFξ within the open unit disk A. Additionally, by employing the technique, the differential sandwich outcome is achieved. Therefore, this work presents crucial exceptional instances that follow the results. The findings of this paper can be applied to a wide range of mathematical and engineering problems, including system identification, orthogonal polynomials, fluid dynamics, signal processing, antenna technology, and approximation theory. Furthermore, this work significantly advances the knowledge and understanding of the analytical functions of the unit and its interactive higher relations. The characteristics and consequences of differential subordination theory are symmetric to those of differential superordination theory. By combining them, sandwich-type theorems can be derived. Full article
(This article belongs to the Special Issue Integral Transformation, Operational Calculus and Their Applications III)
15 pages, 2267 KiB  
Article
Upper Bounds of the Third Hankel Determinant for Bi-Univalent Functions in Crescent-Shaped Domains
by Qasim Ali Shakir, Adel Salim Tayyah, Daniel Breaz, Luminita-Ioana Cotîrlă, Eleonora Rapeanu and Fethiye Müge Sakar
Symmetry 2024, 16(10), 1281; https://doi.org/10.3390/sym16101281 - 29 Sep 2024
Viewed by 859
Abstract
This paper investigates the third Hankel determinant, denoted H3(1), for functions within the subclass RS∑*(λ) of bi-univalent functions associated with crescent-shaped regions φ⦅z=z+1+z2 [...] Read more.
This paper investigates the third Hankel determinant, denoted H3(1), for functions within the subclass RS∑*(λ) of bi-univalent functions associated with crescent-shaped regions φ⦅z=z+1+z2. The primary aim of this study is to establish upper bounds for H3(1). By analyzing functions within this specific geometric context, we derive precise constraints on the determinant, thereby enhancing our understanding of its behavior. Our results and examples provide valuable insights into the properties of bi-univalent functions in crescent-shaped domains and contribute to the broader theory of analytic functions. Full article
(This article belongs to the Special Issue Integral Transformation, Operational Calculus and Their Applications III)
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12 pages, 303 KiB  
Article
Modified Fractional Difference Operators Defined Using Mittag-Leffler Kernels
by Pshtiwan Othman Mohammed, Hari Mohan Srivastava, Dumitru Baleanu and Khadijah M. Abualnaja
Symmetry 2022, 14(8), 1519; https://doi.org/10.3390/sym14081519 - 25 Jul 2022
Cited by 14 | Viewed by 1724
Abstract
The discrete fractional operators of Riemann–Liouville and Liouville–Caputo are omnipresent due to the singularity of the kernels. Therefore, convexity analysis of discrete fractional differences of these types plays a vital role in maintaining the safe operation of kernels and symmetry of discrete delta [...] Read more.
The discrete fractional operators of Riemann–Liouville and Liouville–Caputo are omnipresent due to the singularity of the kernels. Therefore, convexity analysis of discrete fractional differences of these types plays a vital role in maintaining the safe operation of kernels and symmetry of discrete delta and nabla distribution. In their discrete version, the generalized or modified forms of various operators of fractional calculus are becoming increasingly important from the viewpoints of both pure and applied mathematical sciences. In this paper, we present the discrete version of the recently modified fractional calculus operator with the Mittag-Leffler-type kernel. Here, in this article, the expressions of both the discrete nabla derivative and its counterpart nabla integral are obtained. Some applications and illustrative examples are given to support the theoretical results. Full article
(This article belongs to the Special Issue Integral Transformation, Operational Calculus and Their Applications III)
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