An efficient spectral collocation method for the dynamic simulation of the fractional epidemiological model of the Ebola virus

HM Srivastava, KM Saad, MM Khader - Chaos, Solitons & Fractals, 2020 - Elsevier
This article investigates a family of approximate solutions for the fractional model (in the
Liouville-Caputo sense) of the Ebola virus via an accurate numerical procedure (Chebyshev …

Numerical solution of multiterm variable‐order fractional differential equations via shifted Legendre polynomials

AA El‐Sayed, P Agarwal - Mathematical Methods in the …, 2019 - Wiley Online Library
In this paper, shifted Legendre polynomials will be used for constructing the numerical
solution for a class of multiterm variable‐order fractional differential equations. In the …

Eighth-kind Chebyshev polynomials collocation algorithm for the nonlinear time-fractional generalized Kawahara equation

WM Abd-Elhameed, YH Youssri, AK Amin… - Fractal and Fractional, 2023 - mdpi.com
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 …

Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

P Agarwal, AA El-Sayed - Physica A: Statistical Mechanics and Its …, 2018 - Elsevier
In this paper, a new numerical technique for solving the fractional order diffusion equation is
introduced. This technique basically depends on the Non-Standard finite difference method …

An efficient technique for solving the space-time fractional reaction-diffusion equation in porous media

P Pandey, S Kumar, JF Gómez-Aguilar… - Chinese Journal of …, 2020 - Elsevier
In this paper, we obtained the approximate numerical solution of space-time fractional-order
reaction-diffusion equation using an efficient technique homotopy perturbation technique …

Vieta–Fibonacci operational matrices for spectral solutions of variable-order fractional integro-differential equations

P Agarwal, AA El-Sayed, J Tariboon - Journal of Computational and …, 2021 - Elsevier
In this paper, we formulate a numerical method to find out the approximate solution for
fractional integro-differential equations of variable order (FIDE-VO). The methodology that …

New studies for general fractional financial models of awareness and trial advertising decisions

NH Sweilam, MM Abou Hasan, D Baleanu - Chaos, Solitons & Fractals, 2017 - Elsevier
In this paper, two numerical techniques are introduced to study numerically the general
fractional advertising model. This system describes the flux of the consumers from unaware …

On the numerical evaluation for studying the fractional KdV, KdV-Burgers and Burgers equations

MM Khader, KM Saad - The European Physical Journal Plus, 2018 - Springer
This paper is devoted to present an accurate numerical procedure to solve fractional
(Caputo sense) Korteweg-de Vries, Korteweg-de Vries-Burgers and Burgers equations by …

Implementation of an accurate method for the analysis and simulation of electrical R‐L circuits

M Adel, HM Srivastava… - Mathematical Methods in …, 2023 - Wiley Online Library
In this study, we propose to introduce and apply an accurate numerical procedure to solve
the mathematical model of fractional order, which describes the electrical circuits composed …

A numerical study by using the Chebyshev collocation method for a problem of biological invasion: Fractional Fisher equation

MM Khader, KM Saad - International Journal of Biomathematics, 2018 - World Scientific
In this paper, an efficient numerical method is introduced for solving the fractional (Caputo
sense) Fisher equation. We use the spectral collocation method which is based upon …