On Existence and Uniqueness of Solutions for Semilinear Fractional Wave Equations

Let Ω be a C 2 -bounded domain of R d , d = 2,3, and fix Q = (0, T )× Ω with T ∈ (0,+∞). In the present paper we consider a Dirichlet initial-boundary value problem associated to the semilinear fractional wave equation ∂ α t + Au = f b ( u ) in Q where 1 1. Moreover, we obtain an explicit dependence of the time of existence of solutions with respect to the initial data that allows longer time of existence for small initial data.