A hybrid approach for non-linear fractional Newell-Whitehead-Segel model

In this article, we applied the Shehu transform decomposition method (STDM) to obtain the approximate solution of the nonlinear fractional Newell-Whitehead-Segel equation that arises in various physical phenomena, such as fluid mechanics, solid-state physics, optics, plasma physics, dispersion, and chemical kinetics. The fractional NWS model is associated with the temperature and thermal convection of fluid dynamics, aiding in describing the formulation process on liquid surfaces restricted along a horizontally well-conducting boundary. To minimize computing complexity and intricacy, we utilized the proposed method, which combines the Shehu transform and the Adomian decomposition method, to solve the presented model. The results obtained by implementing the suggested method confirm that the solution approaches closer to the exact solution as the value tends from fractional order towards integer order. Moreover, the proposed method is interesting, easy, and highly accurate in solving various nonlinear fractional-order partial differential equations. The numerical results and their graphical simulations are presented using MATLAB