Utilizing an imaginative approach to examine a fractional Newell–Whitehead–Segel equation based on the Mohand HPA

Abstract

This study implemented a novel technique to address the common issue of stripe pattern formation in 2D systems known as the time-fractional Newell–Whitehead–Segel problem. The study presents the Mohand transforms and their properties in conformable sense. The proposed solution involved utilizing the homotopy perturbation approach (HPA) and conformable Mohand transform (CMT) to tackle four case studies of the time-fractional Newell–Whitehead–Segel problem. The graphical outcomes produced by the suggested approach resembled the exact solution. The effectiveness of the suggested techniques was demonstrated by presenting precise and analytical data through graphs. Additionally, the results of using the suggested technique for different values of \(\alpha \) were compared, showing that as the value moves from a fractional order to an integer order, the answer becomes more and more similar to the exact solution.