Strichartz estimates for space-time fractional Schrödinger equations

Abstract

In this paper, we obtain Strichartz type estimates for space-time fractional Schrödinger equations. By making use of the Besov norm and the Mittag-Leffler function, we show that the regularity of the solutions depends on the ratio of the orders of time and space derivatives. In particular, if the ratio equals to 2, it follows that the original Strichartz estimates can be recovered. We also show that the regularity of the solution is sharp in the sense of the Besov norm.