Analytical investigation of fractional-order Newell-Whitehead-Segel equations via a novel transform

In this paper, we find the solution of the time-fractional Newell-Whitehead-Segel equation with the help of two different methods. The newell-Whitehead-Segel equation plays an efficient role in nonlinear systems, describing the stripe patterns' appearance in two-dimensional systems. Four case study problems of Newell-Whitehead-Segel are solved by the proposed methods with the aid of the Antagana-Baleanu fractional derivative operator and the Laplace transform. The numerical results obtained by suggested techniques are compared with an exact solution. To show the effectiveness of the proposed methods, we show exact and analytical results compared with the help of graphs and tables, which are in strong agreement with each other. Also, the results obtained by implementing the suggested methods at various fractional orders are compared, which confirms that the solution gets closer to the exact solution as the value tends from fractional-order towards integer order. Moreover, proposed methods are interesting, easy and highly accurate in solving various nonlinear fractional-order partial differential equations.