The novel numerical solutions for Caputo-Fabruzo fractional Newell–Whitehead–SegelEquation by using Aboodh-ADM

Abstract This article aims to solve Caputo-Fabruzo fractional differential equations using the Aboodh transform together with the Adomian Decomposition method (A-ADM). Since the Aboodh transform can only be applied to linear equations, ADM is an effective technique for approximating solutions of nonlinear differential equations. In nonlinear systems, the Newell-Whitehead-Segel equation plays an important role, explaining the emergence of stripes in 2-dimensional systems. The findings show that the results obtained from the tables provide superior results compared to the existing conformable q-Shehu homotopy analysis transform method (Cq-SHATM) in the literature. With the help of Matlab package program, numerical values were found to depict three-dimensional surfaces and displayed in a table.