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 Newell–Whitehead–Segel 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.

中文翻译：

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求解分数阶 Newell-Whitehead-Segel 方程的混合方法

本文使用Shehu变换结合q-同伦分析变换方法（q-HATM）来求解分数阶微分方程。由于 Shehu 变换仅适用于线性方程，因此 q-HATM 是一种近似非线性微分方程解的有效技术。在解释二维系统中条纹出现的非线性系统中，Newell-Whitehead-Segel 方程发挥着重要作用。研究结果表明，与文献中现有的 LTDM 相比，从表格得出的结果产生了更好的结果。Maple 用于描绘三维表面并查找表格中显示的数值。