In this paper we consider a fractional wave equation for hypoelliptic operators with a singular mass term depending on the spacial variable and prove that it has a very weak solution. Such analysis can be conveniently realised in the setting of graded Lie groups. The uniqueness of the very weak solution, and the consistency with the classical solution are also proved, under suitable considerations. This extends and improves the results obtained in the first part [Altybay et al. Fractional Klein-Gordon equation with singular mass. Chaos Solitons Fractals. 2021;143:Article ID 110579] which was devoted to the classical Euclidean Klein-Gordon equation.

在本文中，我们考虑了具有奇异质量项的亚椭圆算子的分数波动方程，该方程取决于空间变量，并证明它具有非常弱的解。这种分析可以在分级李群的设置中方便地实现。在适当的考虑下，也证明了极弱解的唯一性，以及与经典解的一致性。这扩展并改进了第一部分中获得的结果 [Altybay 等人。具有奇异质量的分数克莱因-戈登方程。混沌孤子分形。2021;143:Article ID 110579]，专门讨论经典的 Euclidean Klein-Gordon 方程。