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.
