Results 81 to 90 of about 696 (218)

The Numerical Approximation of Caputo Fractional Derivatives of Higher Orders Using a Shifted Gegenbauer Pseudospectral Method: A Case Study of Two-Point Boundary Value Problems of the Bagley–Torvik Type

Mathematics
This paper introduces a novel Shifted Gegenbauer Pseudospectral (SGPS) method for approximating Caputo fractional derivatives (FDs) of an arbitrary positive order.
Kareem T. Elgindy
doaj   +1 more source

Fourier–Gegenbauer Integral Galerkin Method for Solving the Advection–Diffusion Equation with Periodic Boundary Conditions

Computation
This study presents the Fourier–Gegenbauer integral Galerkin (FGIG) method, a new numerical framework that uniquely integrates Fourier series and Gegenbauer polynomials to solve the one-dimensional advection–diffusion (AD) equation with spatially ...
Kareem T. Elgindy
doaj   +1 more source

On generalization of extended Gegenbauer polynomials of two variables

, 2021
Ahmed Ali Al-Gonah, Ahmed Ali Atash
openalex   +1 more source

A numerical technique for solving multi-dimensional fractional optimal control problems

Journal of Taibah University for Science, 2018
In this article, we use the operation matrix (OM) of Riemann–Liouville fractional integral of the shifted Gegenbauer polynomials with the Lagrange multiplier method to provide efficient numerical solutions to the multi-dimensional fractional optimal ...
Hoda F. Ahmed
doaj   +1 more source

New Families of Bi-Univalent Functions Governed by Gegenbauer Polynomials

, 2021
Abbas Kareem Wanas
openalex   +2 more sources

Generalized and mixed type Gegenbauer polynomials

Journal of Mathematical Analysis and Applications, 2012
Using the integral representation method and the monomiality principle (see e.g.[\textit{G. Dattoli}, Advanced special functions and applications. Proceedings of the workshop, Melfi, Italy, May 9-12, 1999. Rome: Aracne Editrice. Proc. Melfi Sch. Adv. Top. Math. Phys.
Khan, Subuhi, Al-Gonah, Ahmed Ali, Yasmin, Ghazala   +2 more
openaire   +1 more source

The Orthogonal Riesz Fractional Derivative

Axioms
The aim of this paper is to extend the concept of the orthogonal derivative to provide a new integral representation of the fractional Riesz derivative. Specifically, we investigate the orthogonal derivative associated with Gegenbauer polynomials Cn(ν)(x)
Fethi Bouzeffour
doaj   +1 more source

The Gegenbauer Polynomial Technique: the evaluation of complicated Feynman integrals [PDF]

, 2001
A. V. Kotikov
openalex   +1 more source

Rényi Entropies of Multidimensional Oscillator and Hydrogenic Systems with Applications to Highly Excited Rydberg States. [PDF]

Entropy (Basel), 2022
Dehesa JS.
europepmc   +1 more source

Jaynes-Gibbs Entropic Convex Duals and Orthogonal Polynomials. [PDF]

Entropy (Basel), 2022
Le Blanc R.
europepmc   +1 more source