In this paper, the existence and uniqueness of a solution to a multi-order fractional nonlinear evolution equations system are studied by applying Banach's Fixed Point Theorem and …
YH Youssri, AG Atta - Contemporary Mathematics, 2024 - ojs.wiserpub.com
In this article, we introduce a novel spectral algorithm utilizing Fibonacci polynomials to numerically solve both linear and nonlinear integro-differential equations with fractional …
This study explores the spectral Galerkin approach to solving the space-time Schrödinger, wave, Airy, and beam equations. In order to facilitate the creation of a semi-analytical …
M Fathy, W Abbas - Journal of Advanced Research in Applied …, 2024 - semarakilmu.com.my
The semi-analytic method based on the Galerkin technique with Chebyshev basis is presented in this paper to solve the linear integro-differential equations in the Volterra …
MH Hashim, AJ Harfash - Iranian Journal of Numerical Analysis and …, 2024 - ijnao.um.ac.ir
In this paper, we explore the numerical analysis of the microscale heat equation. We present the characteristics of numerical solutions obtained through both semi-and fully-discrete …
AG Atta, YH Youssri - Mathematical Methods in the Applied Sciences - Wiley Online Library
In this study, we utilize a specific combination of orthogonal Gegenbauer polynomials as basis functions that satisfy homogeneous boundary conditions in the spatial variable and …
E Magdy, AG Atta, GM Moatimid… - … Journal of Modern …, 2024 - World Scientific
This paper employs a numerical method for the numerical treatment of the time fractional Fokker-Planck equation. This method is based on applying the spectral Petrov-Galerkin …