Browsing by Author "Tuncer, Zehra"

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Citation - Scopus: 8
Bessel equation and Bessel function on $\\mathbb{T}(q h)$
(Tubitak, 2022) Ahmet Yantir; BURCU SILINDIR YANTIR; Zehra TUNCER; Yantır, Burcu Sılındır; Tuncer, Zehra; Yantir, Ahmet
This article is devoted to present nabla $(q h)$ -analogues of Bessel equation and Bessel function. In order to construct series solution of nabla $(q h)$ -Bessel equation we present nabla $(q h)$ -analysis regarding nabla generalized quantum binomial nabla $(q h)$ -analogues of Taylor’s formula Gauss’s binomial formula Taylor series analytic functions analytic exponential function with its fundamental properties analytic trigonometric and hyperbolic functions. We emphasize that nabla $(q h)$ -Bessel equation recovers classical $h-and q-discrete$ Bessel equations. In addition we establish nabla $(q h)4 -Bessel function which is expressed in terms of an absolutely convergent series in nabla generalized quantum binomials and intimately demonstrate its reductions. Finally we develop modified nabla $(q h)$ -Bessel equation modified nabla $(q h)$ -Bessel function and its relation with nabla $(q h)$ -Bessel function.
Citation - WoS: 7
Bessel equation and Bessel function on T(q-h)
(Tubitak Scientific & Technological Research Council Turkey, 2022) Ahmet Yantir; Burcu Silindir Yantir; Zehra Tuncer; Yantir, Burcu Silindir; Tuncer, Zehra; Yantir, Ahmet
This article is devoted to present nabla (q h)-analogues of Bessel equation and Bessel function. In order to construct series solution of nabla (q h)-Bessel equation we present nabla (q h)-analysis regarding nabla generalized quantum binomial nabla (q h)-analogues of Taylor's formula Gauss's binomial formula Taylor series analytic functions analytic exponential function with its fundamental properties analytic trigonometric and hyperbolic functions. We emphasize that nabla (q h)-Bessel equation recovers classical h- and q-discrete Bessel equations. In addition we establish nabla (q h)-Bessel function which is expressed in terms of an absolutely convergent series in nabla generalized quantum binomials and intimately demonstrate its reductions. Finally we develop modified nabla (q h)-Bessel equation modified nabla (q h)-Bessel function and its relation with nabla (q h)-Bessel function.
Some special functions and cylindrical diffusion equation on α-time scale
(Walter de Gruyter GmbH, 2025) Burcu Silindir; Zehra Tuncer; Seçil Gergün; Ahmet Yantir; Silindir, Burcu; Yantir, Ahmet; Gergun, Secil; Tuncer, Zehra
This article is dedicated to present various concepts on α -time scale including power series Taylor series binomial series exponential function gamma function and Bessel functions of the first kind. We introduce the α -exponential function as a series examine its absolute and uniform convergence and establish its additive identity by employing the α -Gauss binomial formula. Furthermore we define the α -gamma function and prove α -analogue of the Bohr-Mollerup theorem. Specifically we demonstrate that the α -gamma function is the unique logarithmically convex solution of f (s + 1) = φ (s) f (s) f (1) = 1 where φ (s) refers to the α -number. In addition we present Euler's infinite product form and asymptotic behavior of α -gamma function. As an application we propose α -analogue of the cylindrical diffusion equation from which α -Bessel and modified α -Bessel equations are derived. We explore the solutions of the α -cylindrical diffusion equation using the separation of variables technique revealing analogues of the Bessel and modified Bessel functions of order zero of the first kind. Finally we illustrate the graphs of the α -analogues of exponential and gamma functions and investigate their reductions to discrete and ordinary counterparts. © 2025 Elsevier B.V. All rights reserved.