Results 41 to 50 of about 320 (175)

A Review of Certain Modern Special Functions and Their Applications

Abstract and Applied Analysis, Volume 2026, Issue 1, 2026.
This review article comprehensively analyzes recent developments in the generalization of special functions (SFs) and polynomials via various fractional calculus operators (FCOs), focusing on the analytical properties and applications of extended Hurwitz–Lerch zeta, Wright, and hypergeometric functions.
Hala Abd Elmageed, Mohamed Abdalla, AbdelMaksoud Soliman   +2 more
wiley   +1 more source

COEFFICIENT BOUNDS FOR REGULAR AND BI-UNIVALENT FUNCTIONS LINKED WITH GEGENBAUER POLYNOMIALS

Проблемы анализа, 2021
The main goal of the paper is to initiate and explore two sets of regular and bi-univalent (or bi-Schlicht) functions in 𝔇 = {𝑧 ∈ C : |𝑧| < 1} linked with Gegenbauer polynomials.
S. R. Swamy, S. Yalçın
doaj   +1 more source

Fractional Dynamics of Nonlinear Liquid Dispersion Pattern Drops: A Robust Analytical Study of Modulation Instability and Compacton Structures

Computational and Mathematical Methods, Volume 2026, Issue 1, 2026.
Nonlinear dispersion phenomena in liquid media often lead to the formation of localized structures such as compact wave packets and dispersion drops. The present investigation demonstrates that the proposed analytical framework yields accurate approximate solutions, successfully captures compacton‐like structures, and clearly reveals the critical ...
Yogeshwari F. Patel, Mohammad Izadi, Hany M. Ahmed, Rajesh Kumar   +3 more
wiley   +1 more source

Initial Coefficients Estimates and Fekete–Szegö Inequality Problem for a General Subclass of Bi-Univalent Functions Defined by Subordination

Axioms, 2023
In the present work, we aim to introduce and investigate a novel comprehensive subclass of normalized analytic bi-univalent functions involving Gegenbauer polynomials and the zero-truncated Poisson distribution. For functions in the aforementioned class,
Mohamed Illafe, Feras Yousef, Maisarah Haji Mohd, Shamani Supramaniam   +3 more
doaj   +1 more source

Computational Framework for Numerical Simulation of Fractional‐Order Financial Crime Model via Lucas Collocation Technique

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
The Lucas collocation approach is used in this study to approximate a fractional‐order financial crime model (FOFCM) numerically. The model categorizes the population into five groups: persons without a financial criminal past, those inclined toward financial crimes, active participants, individuals undergoing prosecution, and those imprisoned.
Mahmoud Abd El-Hady, Homan Emadifar, Mehdi Hariri, Atallah El-Shenawy, Chong Lin   +4 more
wiley   +1 more source

Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space

International Journal of Mathematics and Mathematical Sciences, 2004
A new method for constructing Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space is presented. In earlier research, we only dealt with scalar-valued weight functions.
Fred Brackx, Nele De Schepper, Frank Sommen   +2 more
doaj   +1 more source

Fractional Q$Q$‐curvature on the sphere and optimal partitions

Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.
Abstract We study an optimal partition problem on the sphere, where the cost functional is associated with the fractional Q$Q$‐curvature in terms of the conformal fractional Laplacian on the sphere. By leveraging symmetries, we prove the existence of a symmetric minimal partition through a variational approach. A key ingredient in our analysis is a new
Héctor A. Chang‐Lara, Juan Carlos Fernández, Alberto Saldaña   +2 more
wiley   +1 more source

On a Class of Integrals Involving a Bessel Function Times Gegenbauer Polynomials

International Journal of Mathematics and Mathematical Sciences, 2007
We provide information and explicit formulae for a class of integrals involving Bessel functions and Gegenbauer polynomials. We present a simple proof of an old formula of Gegenbauer.
Stamatis Koumandos
doaj   +1 more source

Representation by several orthogonal polynomials for sums of finite products of Chebyshev polynomials of the first, third and fourth kinds

Advances in Difference Equations, 2019
The classical linearization problem concerns with determining the coefficients in the expansion of the product of two polynomials in terms of any given sequence of polynomials.
Taekyun Kim, Dae San Kim, Dmitry V. Dolgy, Dojin Kim   +3 more
doaj   +1 more source

Reconstruction Techniques for Inverse Sturm–Liouville Problems With Complex Coefficients

Mathematical Methods in the Applied Sciences, Volume 48, Issue 17, Page 15875-15889, 30 November 2025.
ABSTRACT A variety of inverse Sturm–Liouville problems is considered, including the two‐spectrum inverse problem, the problem of recovering the potential from the Weyl function, as well as the recovery from the spectral function. In all cases, the potential in the Sturm–Liouville equation is assumed to be complex valued.
Vladislav V. Kravchenko
wiley   +1 more source