Ahmet YantirBURCU SILINDIR YANTIRZehra TUNCERYantır, Burcu SılındırTuncer, ZehraYantir, Ahmet2025-10-222022[1] Bohner M Peterson A. Dynamic Equations on Time Scales Boston USA: Birkhauser 2001.[2] Bohner M Cuchta T. The Bessel difference equation Proceedings of the American Mathematical Society 2017, 145: 1567-1580.[3] Cerm a k J. Nechva tal L On $(q h)$ -analogue of fractional calculus Journal of Nonlinear Mathematical Physics 2010, 17(1): 51-68.[4] Cuchta TJ Discrete analogues of some classical special functions Phd. Thesis Missouri University of Science and Technology 2015.[5] Goldman R Siemonov P. Generalized quantum splines Computer Aided Geometric Design 2016, 47: 29-54.[6] Hahn W. Beitrage zur theorie der Heineschen Reichen Mathematische Nachrichten 1949, 2: 340-379. (in German)[7] Hilger S. Analysis on measure chains–A unified approach to continuous and discrete calculus Results in Mathematics 1990, 18: 18-56.[8] Ismail MEH. The zeros of basic Bessel functions the functions $J_{v+ax}(x)$ and associated orthogonal polynomials Journal of Mathematical Anaysis and Applications 86 (1) (1982) 1-19.[9] Jackson FH. A basic-sine and cosine with sybolical solution of certain differential equations Proceedings of Edinburgh Mathematical Society 1904, 22: 28-39.[10] Jackson FH. The application of basic numbers to Bessel’s and Legendre’s functions Proceedings of the London Mathematical Society 1905, 2: 192-220.[11] Kac V Cheung P. Quantum Calculus Springer 2002.[12] Mahmoud M. Generalized $q -Bessel$ function and its properties Advances in Difference Equations 2013, 2013:121.[13] Rahmat MRS. The $(q h)$ -Laplace transform on discrete time scales Computers and Mathematics with Applications 2011, 62: 272-281.[14] Silindir B Yantir A. Generalized quantum exponential function and its applications Filomat 2019, 33(15): 907- 4922.[15] Silindir B Yantir A. Gauss’s binomial formula and additive property of exponential functions on T$(qh)$ Filomat: 2021, 35(11): 3855-3877.1300-00981303-614910.55730/1300-0098.33342-s2.0-85143798381https://gcris.yasar.edu.tr/handle/123456789/10584https://search.trdizin.gov.tr/en/yayin/detay/1147238https://doi.org/10.55730/1300-0098.3334This 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.İngilizceinfo:eu-repo/semantics/openAccessMatematikH) -Bessel FunctionH) -Taylor SeriesH) -Bessel EquationNabla (qNabla Generalized Quantum BinomialH) -Analytic FunctionsArticle