An approximate solution of a nonlinear fractional differential equation by Adomian decomposition method

Time-fractional KdV equation: formulation and solution using variational methods

“…However, most of these methods are suitable for special types of fractional differential equations, namely the linear with constant coefficients. However, recently there are some papers deal with the existence and multiplicity of solution of nonlinear fractional differential equation using techniques of nonlinear analysis such as fixed-point theorems, Leray-Shauder theory, Adomian decomposition method and variational-iteration method [32][33][34][35][36][37][38]. In this paper, the obtained fractional KdV equation will be solved using the variational-iteration method (VIM), firstly used by He [39][40][41].…”

Convergence Analysis of Variational Iteration Method for Caputo Fractional Differential Equations

“…Many authors have presented many numerical methods for adomian decomposition method, linear multistep method, collocation method, predictor-corrector method, etc. applied to fractional differential equations (see [7][8][9][10][11][12]). …”

A Decomposition Method for Solving the Fractional Davey-Stewartson Equations

“…For most of the FDEs, obtaining the analytical solutions is not easy, thus, the approximation and numerical techniques are utilized to solve them. Some of these methods were Adomian decomposition method (ADM) [1,14,[16][17][18][19], Homotopy perturbation method (HPM) [1,13], Homotopy analysis method (HAM) [11], Variational iteration method (VIM) [10] and so on [2]. Our main aim in the current paper is to apply new iterative method to solve fractional Davey-Stewartson (DS) equations.…”