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

Marianna Chatzakou, Michael V. Ruzhansky, Niyaz Tokmagambetov

2021

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DOI 10.1080/17476933.2021.1950146

Data confidence 70 medium

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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 [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.