The approximate and exact solutions of the space- and time-fractional Burgers equations with initial conditions by variational iteration method

Abstract

In this paper, a scheme is developed to study numerical solution of the space-and timefractional Burgers equations with initial conditions by the variational iteration method (VIM). The exact and numerical solutions obtained by the variational iteration method are compared with that obtained by Adomian decomposition method (ADM). The results show that the variational iteration method is much easier, more convenient, and more stable and efficient than Adomian decomposition method. Numerical solutions are calculated for the fractional Burgers equation to show the nature of solution as the fractional derivative parameter is changed.

Numerical solutions and analysis of diffusion for new generalized fractional Burgers equation

“…In [15], the existence and uniqueness results are proved for the solutions of the stochastic generalized Burgers equations driven by multi-parameter fractional noises. Since many Burgers equations cannot be solved analytically, numerical methods for dealing with them are often required, see [4,7,29,33,14,20,34] and references therein. For instance, Adomian decomposition [4], homotopy analysis [29], variational iteration [14], and integral transform [20], finite difference [12,10,35], and finite element methods [28] are some of them which have been studied extensively recently.…”

On the Solution of Burgers’ Equation with the New Fractional Derivative

“…AbdelSalam et al [25] used fractional Riccati expansion method to solve space-time factional Burgers' equation. M. Inc [26] used a variational iteration method to solve the space and time fractional Burgers' equations.…”

An efficient approach based on radial basis functions for solving stochastic fractional differential equations

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