Lie symmetry analysis, conservation laws and similarity reductions of Newell–Whitehead–Segel equation of fractional order

Abstract

The present paper considers the group analysis of the Newell–Whitehead–Segel equation of fractional order. The important advantage of the article is that for the first time we analyzed the equation for time, space and space–time derivatives of Riemann fractional together. This is based on similarity variables obtained from Lie point symmetry operators of the equation in triple cases. These variables help us to find the reduced equations. Finally, we use the generalized Noether’s theorem of fractional order for finding conservation laws of the equations.