Zobrazeno 1 - 10
of 38
pro vyhledávání: '"Waleed Mohamed Abd-Elhameed"'
Publikováno v:
AIMS Mathematics, Vol 9, Iss 9, Pp 25457-25481 (2024)
This work aims to provide a new Galerkin algorithm for solving the fractional Rayleigh-Stokes equation (FRSE). We select the basis functions for the Galerkin technique to be appropriate orthogonal combinations of the second kind of Chebyshev polynomi
Externí odkaz:
https://doaj.org/article/6e60e1e599db410baade02b76ab2734c
Autor:
Waleed Mohamed Abd-Elhameed
Publikováno v:
AIMS Mathematics, Vol 9, Iss 8, Pp 20058-20088 (2024)
This paper presents a new approach for the unified Chebyshev polynomials (UCPs). It is first necessary to introduce the three basic formulas of these polynomials, namely analytic form, moments, and inversion formulas, which will later be utilized to
Externí odkaz:
https://doaj.org/article/ce1e1bd85b4040128491a72de1bf439f
Publikováno v:
AIMS Mathematics, Vol 9, Iss 1, Pp 2137-2166 (2024)
In this article, we propose two numerical schemes for solving the time-fractional heat equation (TFHE). The proposed methods are based on applying the collocation and tau spectral methods. We introduce and employ a new set of basis functions: The uni
Externí odkaz:
https://doaj.org/article/5c631ea22b864b7e95b175e406e00eeb
Publikováno v:
AIMS Mathematics, Vol 9, Iss 1, Pp 565-593 (2024)
The article investigates a class of polynomials known as convolved Pell polynomials. This class generalizes the standard class of Pell polynomials. New formulas related to convolved Pell polynomials are established. These formulas may be useful in di
Externí odkaz:
https://doaj.org/article/05a4102a02b7401cbac33930f8d5b2ef
Publikováno v:
Fractal and Fractional, Vol 8, Iss 7, p 427 (2024)
This paper analyzes a novel use of the shifted Fibonacci polynomials (SFPs) to treat the time-fractional Burgers equation (TFBE). We first develop the fundamental formulas of these polynomials, which include their power series representation and the
Externí odkaz:
https://doaj.org/article/eed8e621ebc244d79e6171688a64c263
Publikováno v:
AIMS Mathematics, Vol 7, Iss 8, Pp 15138-15158 (2022)
The principal objective of the current paper is to propose a numerical algorithm for treating the linearized time-fractional KdV equation based on selecting two different sets of basis functions. The members of the first set are selected to be suitab
Externí odkaz:
https://doaj.org/article/f2a2032947c64b59b404c436d500ef06
Publikováno v:
AIMS Mathematics, Vol 7, Iss 7, Pp 12962-12980 (2022)
This article deals with a Horadam type of generalized numbers involving four parameters. These numbers generalize several celebrated numbers in the literature such as the generalized Fibonacci, generalized Lucas, Fibonacci, Lucas, Pell, Pell-Lucas, F
Externí odkaz:
https://doaj.org/article/87c49577ff684bdeb69204f266fa1f4d
Publikováno v:
Fractal and Fractional, Vol 7, Iss 9, p 652 (2023)
In this study, we present an innovative approach involving a spectral collocation algorithm to effectively obtain numerical solutions of the nonlinear time-fractional generalized Kawahara equation (NTFGKE). We introduce a new set of orthogonal polyno
Externí odkaz:
https://doaj.org/article/aec6db8bded945f28a41342ac3f09df5
Publikováno v:
Symmetry, Vol 15, Iss 3, p 736 (2023)
In this paper, new formulas for the Fibonacci polynomials, including high-order derivatives and repeated integrals of them, are derived in terms of the polynomials themselves. The results are then used to solve connection problems between the Fibonac
Externí odkaz:
https://doaj.org/article/430c908da44f4b21b028eccdc71bf428
Autor:
Esraa Magdy Abdelghany, Waleed Mohamed Abd-Elhameed, Galal Mahrous Moatimid, Youssri Hassan Youssri, Ahmed Gamal Atta
Publikováno v:
Symmetry, Vol 15, Iss 3, p 594 (2023)
The time-fractional heat equation governed by nonlocal conditions is solved using a novel method developed in this study, which is based on the spectral tau method. There are two sets of basis functions used. The first set is the set of non-symmetric
Externí odkaz:
https://doaj.org/article/e1b3b5d1a527416f968ad2d0c75072b4