[PDF][PDF] A review of the Adomian decomposition method and its applications to fractional differential equations

JS Duan, R Rach, D Baleanu… - … in Fractional Calculus, 2012 - academia.edu
In this article we review the Adomian decomposition method (ADM) and its modifications
including different modified and parametrized recursion schemes, the multistage ADM for …

The third kind Chebyshev wavelets collocation method for solving the time-fractional convection diffusion equations with variable coefficients

F Zhou, X Xu - Applied Mathematics and Computation, 2016 - Elsevier
In this paper, a numerical method based on the third kind Chebyshev wavelets is proposed
for solving a class of time-fractional convection diffusion equations with variable coefficients …

A method based on the Jacobi tau approximation for solving multi-term time–space fractional partial differential equations

AH Bhrawy, MA Zaky - Journal of Computational Physics, 2015 - Elsevier
In this paper, we propose and analyze an efficient operational formulation of spectral tau
method for multi-term time–space fractional differential equation with Dirichlet boundary …

Numerical solution of two-dimensional stochastic time-fractional Sine–Gordon equation on non-rectangular domains using finite difference and meshfree methods

F Mirzaee, S Rezaei, N Samadyar - Engineering Analysis with Boundary …, 2021 - Elsevier
Abstract The nonlinear Sine-Gordon equation is one of the widely used partial differential
equations that appears in various sciences and engineering. The main purpose of writing …

Numerical solution for the variable order linear cable equation with Bernstein polynomials

Y Chen, L Liu, B Li, Y Sun - Applied Mathematics and Computation, 2014 - Elsevier
In this paper, Bernstein polynomials method is proposed for the numerical solution of a class
of variable order fractional linear cable equation. In this paper, we adopted Bernstein …

An implicit RBF meshless approach for solving the time fractional nonlinear sine-Gordon and Klein–Gordon equations

M Dehghan, M Abbaszadeh, A Mohebbi - Engineering Analysis with …, 2015 - Elsevier
In this paper, we propose a numerical method for the solution of time fractional nonlinear
sine-Gordon equation that appears extensively in classical lattice dynamics in the continuum …

[HTML][HTML] Efficient sustainable algorithm for numerical solutions of systems of fractional order differential equations by Haar wavelet collocation method

T Abdeljawad, R Amin, K Shah, Q Al-Mdallal… - Alexandria Engineering …, 2020 - Elsevier
This manuscript deals a numerical technique based on Haar wavelet collocation which is
developed for the approximate solution of some systems of linear and nonlinear fractional …

Fast iterative method with a second-order implicit difference scheme for time-space fractional convection–diffusion equation

XM Gu, TZ Huang, CC Ji, B Carpentieri… - Journal of Scientific …, 2017 - Springer
In this paper we intend to establish fast numerical approaches to solve a class of initial-
boundary problem of time-space fractional convection–diffusion equations. We present a …

Combination of finite difference method and meshless method based on radial basis functions to solve fractional stochastic advection–diffusion equations

F Mirzaee, N Samadyar - Engineering with computers, 2020 - Springer
The present article develops a semi-discrete numerical scheme to solve the time-fractional
stochastic advection–diffusion equations. This method, which is based on finite difference …

[HTML][HTML] Application of the collocation method for solving nonlinear fractional integro-differential equations

MR Eslahchi, M Dehghan, M Parvizi - Journal of Computational and …, 2014 - Elsevier
In this paper, using the collocation method we solve the nonlinear fractional integro-
differential equations (NFIDE) of the form: f (t, y (t), a CD t α 0 y (t),…, a CD t α ry (t))= λ G (t, y …