Nonexistence of Global Weak Solutions of Fractional Pseudo‐Hyperbolic Equations and System in Heisenberg Group

In this paper, we establish sufficient conditions for the nonexistence of global solutions to Cauchy problems involving fractional integro‐pseudohyperbolic equations. These equations involve the fractional Laplacian operator together with the Riemann–Liouville fractional integral and derivative. The nonexistence results are further extended to the associated system of equations, all within the framework of the Heisenberg group. The proofs of nonexistence theorems rely on the nonlinear capacity method, which is implemented through the construction of suitable test functions in the weak formulation of the problems under consideration. This approach provides a unified technique for demonstrating nonexistence in fractional models on non‐Euclidean structures.