Fractional Klein-Gordon equation with singular mass. II: hypoelliptic case

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.

Automated summary

In this paper, a fractional wave equation for hypoelliptic operators with a singular mass term depending on the spatial variable is considered, and a very weak solution is proved. The analysis is conveniently realized in the setting of graded Lie groups. The uniqueness of the very weak solution and its consistency with the classical solution are also demonstrated, extending and improving previous results on the classical Euclidean Klein-Gordon equation.