Results 41 to 50 of about 6,635 (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, Mohammad Ayman-Mursaleen, Hojjatollah Amiri Kayvanloo, Smritijit Sen   +3 more
wiley   +1 more source

Finding identities and q-difference equations for new classes of bivariate q-matrix polynomials

Applied Mathematics in Science and Engineering
This article introduces 2-variable q-Hermite matrix polynomials and delves into their complex representation, unravelling specific outcomes. The exploration encompasses the derivation of insightful identities for the q-cosine and q-sine analogues of the ...
Subuhi Khan, Hassan Ali, Mohammed Fadel
doaj   +1 more source

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, Bayram Çekim, Sezin Çit, Smritijit Sen   +3 more
wiley   +1 more source

Poisson kernels of q$q$‐3D Hermite polynomials expansion for functions of several variables via generalized q$q$‐heat equations

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
wiley   +1 more source

Vanishing Results for Hall-Littlewood Polynomials [PDF]

, 2012
It is well-known that if one integrates a Schur function indexed by a partition λ over the symplectic (resp. orthogonal) group, the integral vanishes unless all parts of λ have even multiplicity (resp. all parts of λ are even).
Venkateswaran, Vidya
core   +1 more source

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, Mahmudov, Nazim I.   +1 more
openaire   +2 more sources

Classical Multiple Orthogonal Polynomials for Arbitrary Number of Weights and Their Explicit Representation

Studies in Applied Mathematics, Volume 154, Issue 3, March 2025.
ABSTRACT This paper delves into classical multiple orthogonal polynomials with an arbitrary number of weights, including Jacobi–Piñeiro, Laguerre of both first and second kinds, as well as multiple orthogonal Hermite polynomials. Novel explicit expressions for general recurrence coefficients, as well as the stepline case, are provided for all these ...
Amílcar Branquinho, Juan E. F. Díaz, Ana Foulquié‐Moreno, Manuel Mañas   +3 more
wiley   +1 more source

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.
openaire   +4 more sources

Orthogonal Laurent Polynomials of Two Real Variables

Studies in Applied Mathematics, Volume 154, Issue 1, January 2025.
ABSTRACT In this paper, we consider an appropriate ordering of the Laurent monomials xiyj$x^{i}y^{j}$, i,j∈Z$i,j \in \mathbb {Z}$ that allows us to study sequences of orthogonal Laurent polynomials of the real variables x$x$ and y$y$ with respect to a positive Borel measure μ$\mu$ defined on R2$\mathbb {R}^2$ such that ({x=0}∪{y=0})∩supp(μ)=∅$(\lbrace ...
Ruymán Cruz‐Barroso, Lidia Fernández
wiley   +1 more source

Application of (q, τ)‐Bernoulli Interpolation to the Spectral Solution of Quantum Differential Equations

International Journal of Differential Equations, Volume 2025, Issue 1, 2025.
In order to solve fractional differential equations on quantum domains, this work provides a spectral approach based on higher‐order (q, τ)‐Bernoulli functions and polynomials. We build a robust basis for approximation in (q, τ)‐weighted Hilbert spaces by using the orthogonality properties of these extended polynomials and the Sheffer‐type generating ...
Shaher Momani, Rabha W. Ibrahim, Khalil Ezzinbi   +2 more
wiley   +1 more source