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

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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.
Keywords
Klein–Gordon equation, Rockland operator, Cauchy problem, graded Lie group, weak solution, very weak solution, WAVE-EQUATION, WEAK SOLUTIONS

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MLA
Chatzakou, Marianna, et al. “Fractional Klein-Gordon Equation with Singular Mass. II: Hypoelliptic Case.” COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, vol. 67, no. 3, 2022, pp. 615–32, doi:10.1080/17476933.2021.1950146.
APA
Chatzakou, M., Ruzhansky, M., & Tokmagambetov, N. (2022). Fractional Klein-Gordon equation with singular mass. II: hypoelliptic case. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 67(3), 615–632. https://doi.org/10.1080/17476933.2021.1950146
Chicago author-date
Chatzakou, Marianna, Michael Ruzhansky, and Niyaz Tokmagambetov. 2022. “Fractional Klein-Gordon Equation with Singular Mass. II: Hypoelliptic Case.” COMPLEX VARIABLES AND ELLIPTIC EQUATIONS 67 (3): 615–32. https://doi.org/10.1080/17476933.2021.1950146.
Chicago author-date (all authors)
Chatzakou, Marianna, Michael Ruzhansky, and Niyaz Tokmagambetov. 2022. “Fractional Klein-Gordon Equation with Singular Mass. II: Hypoelliptic Case.” COMPLEX VARIABLES AND ELLIPTIC EQUATIONS 67 (3): 615–632. doi:10.1080/17476933.2021.1950146.
Vancouver
1.
Chatzakou M, Ruzhansky M, Tokmagambetov N. Fractional Klein-Gordon equation with singular mass. II: hypoelliptic case. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS. 2022;67(3):615–32.
IEEE
[1]
M. Chatzakou, M. Ruzhansky, and N. Tokmagambetov, “Fractional Klein-Gordon equation with singular mass. II: hypoelliptic case,” COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, vol. 67, no. 3, pp. 615–632, 2022.
@article{8754739,
  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.}},
  author       = {{Chatzakou, Marianna and Ruzhansky, Michael and Tokmagambetov, Niyaz}},
  issn         = {{1747-6933}},
  journal      = {{COMPLEX VARIABLES AND ELLIPTIC EQUATIONS}},
  keywords     = {{Klein–Gordon equation,Rockland operator,Cauchy problem,graded Lie group,weak solution,very weak solution,WAVE-EQUATION,WEAK SOLUTIONS}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{615--632}},
  title        = {{Fractional Klein-Gordon equation with singular mass. II: hypoelliptic case}},
  url          = {{http://dx.doi.org/10.1080/17476933.2021.1950146}},
  volume       = {{67}},
  year         = {{2022}},
}

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