Results 41 to 50 of about 1,802,704 (118)
Controllability and Modeling Perspectives of Tempered Ψ‐Caputo Fractional Systems
Journal of Mathematics, Volume 2026, Issue 1, 2026.In this article, we investigated the controllability of fractional dynamical systems (FDS) involving the tempered Ψ‐Caputo fractional derivative (FD). First, we derived the solution representation for this generalized FD with the help of Laplace transform and Mittag–Leffler (M‐L) function.
Inzamamul Haque +3 more
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Multiple Binomial‐Type Operators and Their Approximation Properties
Journal of Mathematics, Volume 2026, Issue 1, 2026.In this paper, we introduce multiple binomial‐type operators (multiple Bernstein–Sheffer operators) and investigate their approximation properties. These properties are analyzed by means of a Korovkin‐type theorem. Furthermore, by using the first and second modulus of continuity together with Peetre’s κ‐functional, we establish the rate of convergence ...
Mehmet Ali Özarslan +3 more
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A $q$-Umbral Approach to $q$-Appell Polynomials
, 2015 In this paper we aim to specify some characteristics of the so called family of $q$-Appell Polynomials by using $q$-Umbral calculus. Next in our study, we focus on $q$-Genocchi numbers and polynomials as a famous member of this family. To do this, firstly we show that any arbitrary polynomial can be written based on a linear combination of $q$-Genocchi
Keleshteri, Marzieh Eini +1 more
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On (self-) reciprocal Appell polynomials: Symmetry and Faulhaber-type polynomials [PDF]
, 2021 The main purpose of this paper is to study generalized (self-) reciprocal Appell polynomials, which play a certain role in connection with Faulhaber-type polynomials.
Kellner, Bernd C.
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Error Estimation for Shifted q‐Szász–Kantorovich Operators and Their Numerical Properties
Journal of Mathematics, Volume 2026, Issue 1, 2026.This paper introduces a novel class of q‐Szász–Mirakjan–Kantorovich operators defined with shifted sequences. Utilizing the basic principles of q‐calculus, we design the King‐type fundamental construction of q‐Szász–Mirakjan–Kantorovich operators and derive their moments and central moments.
Md. Nasiruzzaman +5 more
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Densely generated 2D q-Appell polynomials of Bessel type and q-addition formulas
Boletim da Sociedade Paranaense de Matemática, 2022 The article aims to introduce a densely generated class of $2D$ $q$-Appell polynomials of Bessel type via generating equation and to establish its $q$-determinant form. It is advantageous to consider the $2D$ $q$-Bernoulli, $2D$ $q$-Roger Szeg\"{o} and $2D$ $q$-Al-Salam Carlitz polynomials of Bessel type as their special members.
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?h-GOULD-HOPPER APPELL POLYNOMIALS
, 2021 In this paper, we introduce the Delta(h)-Gould-Hopper Appell polynomials A(n)(x, y; h) via h-Gould-Hopper polynomials G(h)(n)(x, y). These polynomials reduces to Delta(h)-Appell polynomials in the case y = 0, Delta-Appell polynomials in the case y = 0 ...
Yasar, Banu Yilmaz, Ozarslan, Mehmet Ali
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On the ψ− Sheffer F− Polynomials and Their Degenerate Matrices
Journal of Mathematics, Volume 2026, Issue 1, 2026.In this study, we systematically construct a novel framework within umbral calculus by integrating the structures of generalized F‐calculus and degenerate sequences. Utilizing Roman’s foundational approach to umbral calculus, we first introduce a new family of ψ − F− linear functionals and their corresponding ψ − F− differential operators on the ...
Semra Kuş, Smritijit Sen
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A Comprehensive Study on the Class of q-Appell Polynomials [PDF]
, 2015 Doctor of Philosophy in Mathematics. Thesis (Ph.D.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2015. Supervisor: Prof. Dr.
Keleshteri, Marzieh Eini
core
Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract The representation of an analytic function as a series involving q$q$‐polynomials is a fundamental problem in classical analysis and approximation theory [Ramanujan J. 19 (2009), no. 3, 281–303]. In this paper, our investigation is focusing on q$q$‐analog complex Hermite polynomials, which were motivated by Ismail and Zhang [Adv. Appl.
Jian Cao
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