Nonexistence results for ultra-parabolic equations and systems involving fractional Laplacian operator in Heisenberg group

In this paper, sufficient conditions are obtained for the nonexistence of solutions to the Cauchy problems for ultra-parabolic equations involving fractional Laplacian operator. The nonexistence result is also extended to the corresponding system. The results to such problems are derived in the Heisenberg group. The proofs of our nonexistence theorems are based on the nonlinear capacity method. This method is based on the choice of a suitable test function in the weak formulation of the considered problems.