Local/global existence analysis of fractional wave equations with exponential nonlinearity

In this paper, we concern with an exponential nonlinearity for a fractional wave equation in the whole space, we establish the local existence of solutions in a dense subspace of the Orlicz classification. Moreover, we obtain the global existence of solutions for small initial data in lower dimension 1≤d≤3. Our proofs base on the analyticity of Mittag-Leffler functions, the framework of prior estimates and the type of exponential nonlinearity.