Strichartz estimates for structurally damped equations of space-time-fractional type

Abstract

We obtain Strichartz estimates for a wide class of space-time fractional evolution equations arising in applications towards the theory of structural damping plate equations. We focus on the case where the damping term is described in terms of the time fractional derivative of order alpha taken in the Caputo-Djrbashian sense and of the fractional Laplacian of order sigma in the space variable. Our results heavily rely on the study of the pseudo-differential representation for the resolvent in terms of the Mittag-Leffler functions.