A hybrid method to solve a fractional-order Newell–Whitehead–Segel equation release_howope7h4bak3p7alotfaab3lq

by Umut Bektaş, Halil ANAÇ

Published in Boundary Value Problems by Springer Science and Business Media LLC.

2024   Volume 2024, Issue 1

Abstract

<jats:title>Abstract</jats:title>This paper solves fractional differential equations using the Shehu transform in combination with the q-homotopy analysis transform method (q-HATM). As the Shehu transform is only applicable to linear equations, q-HATM is an efficient technique for approximating solutions to nonlinear differential equations. In nonlinear systems that explain the emergence of stripes in 2D systems, the <jats:italic>Newell–Whitehead–Segel</jats:italic> equation plays a significant role. The findings indicate that the outcomes derived from the tables yield superior results compared to the existing LTDM in the literature. Maple is utilized to depict three-dimensional surfaces and find numerical values that are displayed in a table.
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