Special Issue "Trend Topics in Special Functions and Polynomials: Theory, Methods, Applications and Modeling"

Submission Deadline: 31 December 2021 (closed)
Guest Editors
Dr. Serkan Araci, Hasan Kalyoncu University, Turkey
Prof. Dr. Juan Luis García Guirao, Universidad Politécnica de Cartagena, Spain


The computers began to appear in the 1950s, and often incorrect, estimations were done related to the impact of these devices on applied mathematics, science and engineering. One of these estimations was that the need for special functions, or higher transcendental functions (as they are also known), would disappear entirely. This was based on the observation that the key use of these functions in those days was to approximate the solutions of classical differential (or partial differential) equations: with the mathematical software it would become possible to solve these equations by direct numerical methods. This observation is in fact correct; even so, a study of current computational journals in the sciences reveals a continuous need for numerical algorithms to generate Airy functions, Bessel functions, Coulomb wave functions, error functions and exponential integrals, etc.

This special issue focuses on the applications and computer modeling of the special functions and polynomials to various areas of mathematics. Thorough knowledge of special functions is required in modern engineering, physical science applications and computer modeling. These functions typically arise in such applications as communications systems, statistical probability distribution, electro-optics, nonlinear wave propagation, electromagnetic theory, potential theory, electric circuit theory, and quantum mechanics.

Potential topics include but are not limited to the following:

 Computer modeling of Special functions and polynomials

 Analytical properties and applications of Special functions.

 Inequalities for Special Functions

 Integration of  products of Special Functions

 Properties of ordinary and general families of Special Polynomials

 Operational techniques involving Special Polynomials

 Classes of mixed Special Polynomials and their properties

 Other miscellaneous applications of Special Functions and Special Polynomials

Hypergeometric functions and their extensions; Generalized functions and their extensions; Generalized inequalities and their extensions; Operational techniques; Mixed special polynomials; Applications; Computer modeling.

Published Papers

  • Image Encryption Algorithm Based on New Fractional Beta Chaotic Maps
  • Abstract In this study, a new algorithm of fractional beta chaotic maps is proposed to generate chaotic sequences for image encryption. The proposed technique generates multi random sequences by shuffling the image pixel position. This technique is used to blur the pixels connecting the input and encrypted images and to increase the attack resistance. The proposed algorithm makes the encryption process sophisticated by using fractional chaotic maps, which hold the properties of pseudo-randomness. The fractional beta sequences are utilized to alter the image pixels to decryption attacks. The experimental results proved that the proposed image encryption algorithm successfully encrypted and decrypted… More
  •   Views:891       Downloads:311        Download PDF

  • Degenerate s-Extended Complete and Incomplete Lah-Bell Polynomials
  • Abstract Degenerate versions of special polynomials and numbers applied to social problems, physics, and applied mathematics have been studied variously in recent years. Moreover, the (s-)Lah numbers have many other interesting applications in analysis and combinatorics. In this paper, we divide two parts. We first introduce new types of both degenerate incomplete and complete s-Bell polynomials respectively and investigate some properties of them respectively. Second, we introduce the degenerate versions of complete and incomplete Lah-Bell polynomials as multivariate forms for a new type of degenerate s-extended Lah-Bell polynomials and numbers respectively. We investigate relations between these polynomials and degenerate incomplete and… More
  •   Views:1341       Downloads:574        Download PDF

  • Modeling the Spread of Tuberculosis with Piecewise Differential Operators
  • Abstract Very recently, a new concept was introduced to capture crossover behaviors that exhibit changes in patterns. The aim was to model real-world problems exhibiting crossover from one process to another, for example, randomness to a power law. The concept was called piecewise calculus, as differential and integral operators are defined piece wisely. These behaviors have been observed in the spread of several infectious diseases, for example, tuberculosis. Therefore, in this paper, we aim at modeling the spread of tuberculosis using the concept of piecewise modeling. Several cases are considered, conditions under which the unique system solution is obtained are presented… More
  •   Views:1275       Downloads:695        Download PDF

  • k-Order Fibonacci Polynomials on AES-Like Cryptology
  • Abstract The Advanced Encryption Standard (AES) is the most widely used symmetric cipher today. AES has an important place in cryptology. Finite field, also known as Galois Fields, are cornerstones for understanding any cryptography. This encryption method on AES is a method that uses polynomials on Galois fields. In this paper, we generalize the AES-like cryptology on 2 × 2 matrices. We redefine the elements of k-order Fibonacci polynomials sequences using a certain irreducible polynomial in our cryptology algorithm. So, this cryptology algorithm is called AES-like cryptology on the k-order Fibonacci polynomial matrix. More
  •   Views:731       Downloads:530        Download PDF

  • On ev and ve-Degree Based Topological Indices of Silicon Carbides
  • Abstract In quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies, computation of topological indices is a vital tool to predict biochemical and physio-chemical properties of chemical structures. Numerous topological indices have been inaugurated to describe different topological features. The ev and ve-degree are recently introduced novelties, having stronger prediction ability. In this article, we derive formulae of the ev-degree and ve-degree based topological indices for chemical structure of Si2C3I[a,b]. More
  •   Views:576       Downloads:479       Cited by:1        Download PDF

  • Study of Degenerate Poly-Bernoulli Polynomials by λ-Umbral Calculus
  • Abstract Recently, degenerate poly-Bernoulli polynomials are defined in terms of degenerate polyexponential functions by Kim-Kim-Kwon-Lee. The aim of this paper is to further examine some properties of the degenerate poly-Bernoulli polynomials by using three formulas from the recently developed ‘λ-umbral calculus.’ In more detail, we represent the degenerate poly-Bernoulli polynomials by Carlitz Bernoulli polynomials and degenerate Stirling numbers of the first kind, by fully degenerate Bell polynomials and degenerate Stirling numbers of the first kind, and by higherorder degenerate Bernoulli polynomials and degenerate Stirling numbers of the second kind. More
  •   Views:1528       Downloads:1029       Cited by:2        Download PDF