In the present research article, we implemented two well-known analytical techniques to solve fractional-order multi-dimensional Navier–Stokes equation. The proposed methods are the modification of Adomian decomposition method and variational iteration method by using natural transformation. Furthermore, some illustrative examples are presented to confirm the validity of the suggested methods. The solutions graphs and tables are constructed for both fractional and integer-order problems. It is investigated that the suggested techniques have the identical solutions of the problems. The solution comparison via graphs and tables have also supported the greater accuracy and higher rate of convergence of the present methods.

在本研究文章中，我们实施了两种著名的分析技术来求解分数阶多维Navier–Stokes方程。所提出的方法是通过自然变换对Adomian分解方法和变分迭代方法进行的改进。此外，提供了一些说明性示例以确认所建议方法的有效性。解决方案图形和表格适用于分数阶和整数阶问题。研究表明，所提出的技术具有相同的问题解决方案。通过图形和表格进行的解决方案比较还支持了本方法的更高准确性和更高收敛速度。