Modified residual power series approach for the computational results of Newell-Whitehead-Segel model with fractal derivatives

Abstract

In the current work, we provide the modified residual power series approach to obtain the fractal solution of the Newell-Whitehead-Segel (NWS) model with fractal derivatives. The proposed strategy relies on the two-scale fractal scheme and residual power series scheme (RPSS) that systematically produces the fractal solution in a convergent power series without the need for any constraint parameters. Three numerical applications are provided to display the validity, authenticity, and robustness of the suggested scheme. The connectivity between the fractal solution and the exact solution has been demonstrated by plotted and numerical findings. The 2D and 3D graphical visuals demonstrate the physical behavior of the NWS fractal model at various fractional orders. It is worth noticing that the behavior of the solution demonstrates that changing the fractal parameter reflects the nature of the solution and yields the exact solution very rapidly.