Spectral and discontinuous spectral element methods for fractional delay equations

M Zayernouri, W Cao, Z Zhang, GE Karniadakis - SIAM Journal on Scientific …, 2014 - SIAM
We first develop a spectrally accurate Petrov--Galerkin spectral method for fractional delay
differential equations (FDDEs). This scheme is developed based on a new spectral theory …

Optimal error estimates of spectral Petrov--Galerkin and collocation methods for initial value problems of fractional differential equations

Z Zhang, F Zeng, GE Karniadakis - SIAM Journal on Numerical Analysis, 2015 - SIAM
We present optimal error estimates for spectral Petrov--Galerkin methods and spectral
collocation methods for linear fractional ordinary differential equations with initial value on a …

Numerical solution of unsteady state fractional advection–dispersion equation

N Abeye, M Ayalew, DL Suthar… - Arab Journal of Basic …, 2022 - Taylor & Francis
In this article, we find the numerical solution of unsteady state fractional order advection–
dispersion equation. For an approximate solution of the proposed problem, we apply …

Numerical studies for solving fractional Riccati differential equation

NH Sweilam, MM Khader… - Applications and …, 2012 - digitalcommons.pvamu.edu
In this paper, finite difference method (FDM) and Pade'-variational iteration method (Pade'-
VIM) are successfully implemented for solving the nonlinear fractional Riccati differential …

A method for fractional Volterra integro-differential equations by Laguerre polynomials

D Varol Bayram, A Daşcıoğlu - Advances in Difference Equations, 2018 - Springer
The main purpose of this study is to present an approximation method based on the
Laguerre polynomials for fractional linear Volterra integro-differential equations. This …

The use of generalized Laguerre polynomials in spectral methods for solving fractional delay differential equations

MM Khader - Journal of computational and …, 2013 - asmedigitalcollection.asme.org
In this paper, an efficient numerical method for solving the fractional delay differential
equations (FDDEs) is considered. The fractional derivative is described in the Caputo sense …

Two-dimensional nonlinear time fractional reaction–diffusion equation in application to sub-diffusion process of the multicomponent fluid in porous media

P Pandey, S Das, EM Craciun, T Sadowski - Meccanica, 2021 - Springer
In the present article, an efficient operational matrix based on the famous Laguerre
polynomials is applied for the numerical solution of two-dimensional non-linear time …

[PDF][PDF] Numerical solution of fractional integro-differential equations by least squares method and shifted Laguerre polynomials pseudo-spectral method

AMS Mahdy, RT Shwayyea - International Journal of Scientific …, 2016 - repository.qu.edu.iq
Numerical solution of fractional integro-di erential equations by least squares method and
shifted Laguerre polynomials pseudo-s Page 1 International Journal of Scientific & Engineering …

An operational matrix for solving time-fractional order Cahn-Hilliard equation

P Pandey, S Kumar, H Jafari, S Das - 2019 - idr-lib.iitbhu.ac.in
In the present scientific work, an operational matrix scheme with Laguerre polynomials is
applied to solve a space-time fractional order non-linear Cahn-Hilliard equation, which is …

Spectral collocation method for multi-order fractional differential equations

F Ghoreishi, P Mokhtary - International Journal of Computational …, 2014 - World Scientific
In this paper, the spectral collocation method is investigated for the numerical solution of
multi-order Fractional Differential Equations (FDEs). We choose the orthogonal Jacobi …