In this paper, the fractional-order model is used to study dust acoustic rogue waves in dusty plasma. Firstly, based on control equations, the multi-scale analysis and reduced perturbation method are used to derive the (3+1)-dimensional modified Kadomtsev–Petviashvili (MKP) equation. Secondly, using the semi-inverse method and the fractional variation principle, the (3+1)-dimensional time-fractional modified Kadomtsev–Petviashvili (TF-MKP) equation is derived. Then, the Riemann–Liouville fractional derivative is used to study the symmetric property and conservation laws of the (3+1)-dimensional TF-MKP equation. Finally, the exact solution of the (3+1)-dimensional TF-MKP equation is obtained by using fractional order transformations and the definition and properties of Bell polynomials. Based on the obtained solution, we analyze and discuss dust acoustic rogue waves in dusty plasma.

本文使用分数阶模型研究尘埃等离子体中的尘埃流氓波。首先，基于控制方程，使用多尺度分析和减少摄动法来推导（3 + 1）维改进的Kadomtsev–Petviashvili（MKP）方程。其次，使用半反方法和分数变分原理，推导了（3 + 1）维时间分数修正的Kadomtsev–Petviashvili（TF-MKP）方程。然后，使用黎曼-利维尔分数导数研究（3 + 1）维TF-MKP方程的对称性质和守恒律。最后，利用分数阶变换以及Bell多项式的定义和性质，获得了（3 + 1）维TF-MKP方程的精确解。根据获得的解决方案，