Variational Iteration Method for a Fractional-Order Brusselator System

Abstract

This paper presents approximate analytical solutions for the fractional-order Brusselator system using the variational iteration method. The fractional derivatives are described in the Caputo sense. This method is based on the incorporation of the correction functional for the equation. Two examples are solved as illustrations, using symbolic computation. The numerical results show that the introduced approach is a promising tool for solving system of linear and nonlinear fractional differential equations.

Approximate Analytical Solutions of the Fractional-Order Brusselator System Using the Polynomial Least Squares Method

“…In Figures 1 and 2 we compare these approximations with the corresponding approximations of the same order computed by VIM (relations (15) in [20]), obtaining a good agreement. In Figures 3 and 4 we compare the expressions of remainders (4) obtained by replacing the approximate solutions back in the equations.…”

“…In [20] approximate solutions of (17) are computed using the Variational Iteration Method (VIM) for the case 1 = 2 = 0.98. Also, a comparison with numerical solutions is presented for the particular case 1 = 2 = 1, illustrating the applicability of the method.…”

“…However, in the case 1 = 2 = 1 it is possible to compute the absolute error corresponding to an approximate solution as the difference in absolute value between the approximate solution and the numerical solution (in this case computed by using the Wolfram Mathematica software). Figures 5 and 6 present the comparison between the absolute errors corresponding to the approximate solutions from [20] obtained by VIM and the absolute errors corresponding to our approximate solutions.…”

“…In the next section we will introduce PLSM for the Brusselator system and in the third section we will compare the approximate solutions obtained by using PLSM with the approximate solutions from [20]. The computations show that the approximations computed by using our method present an error smaller than the error of the corresponding solutions from [20].…”

Fractional diffusion equation in half-space with Robin boundary condition

“…It has been applied to many fields in science and engineering, such as viscoelasticity, anomalous diffusion, fluid mechanics, biology, chemistry, acoustics, control theory, etc. In recent years, fractional differential equations have attracted much attention and some analytical methods have been proposed [3][4][5][6][7][8][9][10][11][12][13][14].…”