In this paper, we first created a fractal Date–Jimbo–Kashiwara–Miwa (FDJKM) long ripple wave model in a non-smooth boundary or microgravity space recorded. Using fractal semi-inverse skill (FSIS) and fractal traveling wave transformation (FTWT), the fractal variational principle (FVP) was derived, and the strong minimum necessary circumstance was attested with the He Wierstrass function. We have discovered two distinct solitary wave solutions, the square form of the hyperbolic secant function and the hyperbolic secant function form. Then, soliton solutions are cultivated through FVP and the minimum steady state condition. Finally, the influences of non-smooth boundaries on solitons were tackled, and the properties of the solution were demonstrated through three-dimensional contour lines. Fractal dimension can impact waveforms, but cannot affect their vertex values. The presentation of soliton solutions (SWS) using techniques is not only laudable but also noteworthy. The technique employed can also be used to investigate solitary wave solutions of other local fractional calculus partial differential equations.

在本文中，我们首先在记录的非光滑边界或微重力空间中创建了分形 Date-Jimbo-Kashiwara-Miwa (FDJKM) 长波纹波模型。利用分形半逆技术（FSIS）和分形行波变换（FTWT）推导了分形变分原理（FVP），并用He Wierstrass函数证明了强最小必要条件。我们发现了两种不同的孤立波解，即双曲正割函数的平方形式和双曲正割函数形式。然后，通过FVP和最小稳态条件培养孤子解。最后，解决了非光滑边界对孤子的影响，并通过三维轮廓线展示了解的性质。分形维数可以影响波形，但不能影响其顶点值。使用技术提出的孤子解（SWS）不仅值得称赞，而且值得注意。所采用的技术还可用于研究其他局部分数阶微积分偏微分方程的孤立波解。