Abstract
<p style='text-indent:20px;'>We establish necessary conditions for the existence of global weak solutions to a class of semilinear time-fractional wave inequalities with nonlinearity of derivative type, defined on complete noncompact Riemannian manifolds. A potential function depending of both time and space, is allowed in front of the power nonlinearity. The obtained conditions depend on the parameters of the problem, the initial conditions and the geometry of the manifold. Our results are new even in the Euclidean case.</p>
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