Applications of Special Functions in Complex Analysis and Their Symmetries

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

Deadline for manuscript submissions: 30 June 2025 | Viewed by 423

Special Issue Editors


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Guest Editor

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Guest Editor
Department of Applied Mathematics and Science, College of Engineering, National University of Science & Technology, Al-Hail, Muscat P.O. Box 620, Oman
Interests: geometric function theory and its applications; differential subordination and superordination; complex analysis; univalent functions; special functions

Special Issue Information

Dear Colleagues,

The theory of special functions is very much an application-driven field, and it ranges across all areas of mathematics–pure or applied. For example, the Mittag–Leffler function, which is a special transcendental function, has gained attention due to its application in time-fractional differential equations and boundary value problems. The purpose of this Special Issue is to collect the recent advancements in the field of complex analysis studied in tandem with any of the non-Newtonian calculus/special functions. In keeping with the main theme of the journal, studies pertaining to analytic functions with respect to symmetric points are most welcome.

The topics to be covered include, but are not restricted to, the following:

  • Applications of symmetric functions involving differential and integral operators.
  • Applications of non-Newtonian calculus like multiplicative calculus/quantum calculus in complex analysis.
  • Applications of fractional calculus and special functions in differential subordinations and superordinations.
  • New subclasses of univalent, bi-univalent, starlike, and convex functions.
  • New subclasses of analytic functions with respect to symmetric points.

Prof. Dr. Valer-Daniel Breaz
Dr. Kadhavoor Ragavan Karthikeyan
Guest Editors

Manuscript Submission Information

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Keywords

  • univalent functions
  • multivalent functions
  • special functions
  • multiplicative calculus
  • quantum calculus
  • differential subordination
  • differential superordination
  • fuzzy differential subordinations and superordinations

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Published Papers (1 paper)

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Research

15 pages, 1001 KiB  
Article
Similarity Solutions of Partial Differential–Integral Equations from the Theory of Stochastic Processes
by Mario Lefebvre
Symmetry 2025, 17(5), 704; https://doi.org/10.3390/sym17050704 - 5 May 2025
Viewed by 164
Abstract
First-exit problems are studied for two-dimensional diffusion processes with jumps according to a Poisson process. The size of the jumps is distributed as an exponential random variable. We are interested in the random variable that denotes the first time that the sum of [...] Read more.
First-exit problems are studied for two-dimensional diffusion processes with jumps according to a Poisson process. The size of the jumps is distributed as an exponential random variable. We are interested in the random variable that denotes the first time that the sum of the two components of the process leaves a given interval. The function giving the probability that the process will leave the interval on its left-hand side satisfies a partial differential–integral equation. This equation is solved analytically in particular cases by making use of the method of similarity solutions. The problem of calculating the mean and the moment-generating function of the first-passage time random variable is also considered. The results obtained have applications in various fields, notably, financial mathematics and reliability theory. Full article
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