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

TL;DR

This paper studies a fractional wave equation with hypoelliptic operators and singular mass terms on graded Lie groups, proving existence, uniqueness, and consistency of very weak solutions, extending previous Euclidean results.

Contribution

It introduces a framework for analyzing fractional wave equations with singular mass on graded Lie groups, extending classical Euclidean results to hypoelliptic settings.

Findings

Existence of very weak solutions for the fractional hypoelliptic wave equation.

Uniqueness and consistency of solutions with classical cases.

Extension of previous Euclidean results to graded Lie groups.

Abstract

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 of this work which was devoted to the classical Euclidean Klein-Gordon equation.