Asymptotic-sequentially solution style for the generalized Caputo time-fractional Newell–Whitehead–Segel system

Abstract

The Caputo fractional version of the generalized Newell–Whitehead–Segel model is considered. We introduced a numerical scheme to solve analytically the proposed application. We updated the style of the generalized Taylor series for a reliable treatment of the time-fractional derivative. The effect of the fractional derivative is explored on the obtained solutions for different cases of the problem. A sequential-asymptotic phenomenon has been observed upon varying the order of the fractional derivative from no-memory “ $\alpha=0$ ” to full-memory “ $\alpha=1$ ”.