A new study on the Newell-Whitehead-Segel equation with CaputoFabrizio fractional derivative

Abstract

In this research, we propose a new numerical method that combines with the CaputoFabrizio Elzaki transform and the q-homotopy analysis transform method. This work aims to analyze the Caputo-Fabrizio fractional Newell-Whitehead-Segel (NWS) equation utilizing the CaputoFabrizio q-Elzaki homotopy analysis transform method. The Newell-Whitehead-Segel equation is a partial differential equation employed for modeling the dynamics of reaction-diffusion systems, specifically in the realm of pattern generation in biological and chemical systems. A convergence analysis of the proposed method was performed. Two-dimensional and three-dimensional graphs of the solutions have been drawn with the Maple software. It is seen that the resulting proposed method is more powerful and effective than the Aboodh transform homotopy perturbation method and conformable Laplace decomposition method in the results.