Solving Time Fractional Newell-Whitehead-Segel Equation Via Conformable Variation Iteration Method

Abstract

This study presents the application of the conformable variational iteration method to get approximate analytical solutions for the time fractional Newell-Whitehead-Segel equation. Time fractional order derivative Newell-Whitehead-Segel equation is the interaction of the effect of the diffusion term with the non-linear effect of the reaction term and it is one of the most important of amplitude equation which describes the appearance of the stripe pattern in two dimensional systems A powerful mathematical method known as the C-VIM combines the application of the newly defined fractional derivative introduced by Khalil et al. (2014) called conformable fractional derivative on a well-known variational iteration method. The conformable derivative is one of the admirable choices to handle nonlinear physical problems of different fields of interest. By applying the C-VIM, we derive an approximate analytical solution of time fractional order derivative Newell-Whitehead-Segel equation. Convergence analysis and numerical examples are presented to show the efficiency of the proposed method. Plotted graphs demonstrate the mightiness and accurateness of the proposed technique. The applications show that C-VIM gives solutions that coincide with the exact solutions, and it saves a lot of computational work in solving time fractional NWSEs.