Results 131 to 140 of about 441,925 (264)

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

Quantum algebra approach to q Gegenbauer polynomials

Journal of Computational and Applied Mathematics, 1995
Quantum algebras provide a natural algebraic setting for \(q\)-special functions. The matrix elements of certain algebra generators in irreducible representations are in fact expressible in terms of \(q\)- hypergeometric series. The author here takes the quantum algebra \({\mathcal U}_q (\text{su} (1,1))\) as example, to show that its metaplectic ...
Roberto Floreanini, Luc Vinet
openaire   +4 more sources

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

Optimal Control of a Parabolic Distributed Parameter System Using a Barycentric Shifted Gegenbauer Pseudospectral Method

, 2016
In this paper, we introduce a novel pseudospectral method for the numerical solution of optimal control problems governed by a parabolic distributed parameter system.
Elgindy, Kareem T.
core  

A four dimensional Bernstein Theorem

, 2019
We prove a four dimensional version of the Bernstein Theorem, with complex polynomials being replaced by quaternionic polynomials. We deduce from the theorem a quaternionic Bernstein's inequality and give a formulation of this last result in terms of ...
Perotti, Alessandro
core  

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

An integral formula for generalized Gegenbauer polynomials and Jacobi polynomials

Advances in Applied Mathematics, 2002
In this interesting paper the author studies generalized Gegenbauer polynomials that are orthogonal with respect to the weight function \(|x|^{2\mu}\) \((1-x^2)^{\lambda- {1\over 2}}\). First, an important integral formula is established for these polynomials that serves as a transformation between \(h\)-harmonics of different parameters and contains ...
openaire   +1 more source

Linearization and connection formulae involving squares of gegenbauer polynomials

Applied Mathematics Letters, 2001
Zbl#: Zbl 0978 ...
Jorge Sánchez-Ruiz, Jorge Sánchez-Ruiz
openaire   +4 more sources

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

Functionals of Gegenbauer polynomials and D-dimensional hydrogenic momentum expectation values [PDF]

, 2000
Walter Van Assche, R. J. Yáñez, Rosario González‐Férez, J. S. Dehesa   +3 more
openalex   +1 more source