The present work implements the unified method to a class of fractional partial differential systems corresponding to modified fractional three wave interaction equations (FTWIEs). The fractional derivative of the three waves envelopes is considered under the conformable sense. The conformable FTWIEs is derived in the (3 + 1) dimensions under the conformable time-fractional derivative of order $\alpha \in (0,1]$ based on a modification of the Lax-pair created by Zakharov-Manakov which includes three-dimensional velocity vector dotted with the usual del operator. Then, the unified method for creating solutions for nonlinear evolution FTWIEs is applied. Subsequently, a systematic algorithm is used to obtain an infinite set of exact rational solutions to the novel constructed system. By randomly selecting the special values for the parameters, three-dimensional graphs are also given for different patterns. The obtained solutions might play an essential role in many other nonlinear evolution equations that occur in the fields of engineering and mathematical physics.

本工作将统一方法实现到一类分数偏微分系统，该系统对应于修正的分数三波相互作用方程（FTWIE）。三个波包络的分数导数在顺应意义上考虑。合格的FTWIE在（3 + 1）维中的合格时间分数阶导数下导出$\alpha \in （0，\mathrm{1个}]$基于Zakharov-Manakov创建的Lax对的修改，其中包括用常规del运算符点缀的三维速度矢量。然后，采用统一的方法来创建非线性演化FTWIE的解。随后，使用系统的算法来获得无限的精确构造的有理解。通过随机选择参数的特殊值，还可为不同的模式提供三维图形。所获得的解可能在工程和数学物理学领域中出现的许多其他非线性演化方程中起重要作用。