Abstract
We establish necessary conditions for the existence of global weak solutions to a class of semilinear time-fractional wave inequalities with nonlin-earity of derivative type, defined on complete noncompact Riemannian man-ifolds. A potential function depending of both time and space, is allowed in front of the power nonlinearity. The obtained conditions depend on the param-eters of the problem, the initial conditions and the geometry of the manifold. Our results are new even in the Euclidean case.