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”.
Highlights
Nonlinear physical models with involved time-fractional derivative exhibited an oscillatory or chaotic or pattern states
We aim to explore some of the aforementioned aspects of the fractional derivative if it is considered instead of the integer derivative
We consider the time-fractional version of Newell–Whitehead–Segel (NWS) [2,3,4,5], which reads
Summary
Nonlinear physical models with involved time-fractional derivative exhibited an oscillatory or chaotic or pattern states. These states occur due to a change in the order of the fractional order varying from 0 to 1. It has been stated in [1] that most of the dynamicalphysical models with involved fractional derivatives may possess kind of hereditary features, processes or memory. The fractional NWS equation given in (1.1) with α being the Jumarie derivative has been considered in [8] and the Jumarie fractional complex transform combined with He’s
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