Vieta–Lucas polynomials for solving a fractional-order mathematical physics model

P Agarwal, AA El-Sayed - Advances in Difference Equations, 2020 - Springer
In this article, a fractional-order mathematical physics model, advection–dispersion equation
(FADE), will be solved numerically through a new approximative technique. Shifted Vieta …

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 …

A novel Jacobi operational matrix for numerical solution of multi-term variable-order fractional differential equations

AA El-Sayed, D Baleanu, P Agarwal - Journal of Taibah University …, 2020 - Taylor & Francis
In this article, we introduce a numerical technique for solving a class of multi-term variable-
order fractional differential equation. The method depends on establishing a shifted Jacobi …

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 …

Fractional-order advection-dispersion problem solution via the spectral collocation method and the non-standard finite difference technique

NH Sweilam, AAE El-Sayed, S Boulaaras - Chaos, Solitons & Fractals, 2021 - Elsevier
In this article, a numerical method for solving a fractional-order Advection-Dispersion
equation (FADE) is proposed. The fractional-order derivative of the main problem is …

Enhanced shifted Jacobi operational matrices of derivatives: spectral algorithm for solving multiterm variable-order fractional differential equations

HM Ahmed - Boundary Value Problems, 2023 - Springer
This paper presents a new way to solve numerically multiterm variable-order fractional
differential equations (MTVOFDEs) with initial conditions by using a class of modified shifted …

Finite‐time stability of linear Caputo‐Katugampola fractional‐order time delay systems

A Ben Makhlouf, AM Nagy - Asian Journal of Control, 2020 - Wiley Online Library
Finite‐Time Stability of Linear Caputo‐Katugampola Fractional‐Order Time Delay Systems -
Ben Makhlouf - 2020 - Asian Journal of Control - Wiley Online Library Skip to Article Content …

Chebyshev cardinal wavelets for nonlinear variable-order fractional quadratic integral equations

MH Heydari - Applied Numerical Mathematics, 2019 - Elsevier
This study deals with a computational scheme based on the Chebyshev cardinal wavelets
for a new class of nonlinear variable-order (VO) fractional quadratic integral equations …

Fractional-order Chelyshkov wavelet method for solving variable-order fractional differential equations and an application in variable-order fractional relaxation system

HTB Ngo, M Razzaghi, TN Vo - Numerical Algorithms, 2023 - Springer
We give an efficient numerical approach to solve variable-order fractional differential
equations (VO-FDEs) by applying fractional-order generalized Chelyshkov wavelets …

Numerical solution of nonlinear delay differential equations of fractional variable-order using a novel shifted Jacobi operational matrix

HR Khodabandehlo, E Shivanian… - Engineering with …, 2022 - Springer
This paper presents the generalized nonlinear delay differential equations of fractional
variable-order. In this article, a novel shifted Jacobi operational matrix technique is …