Dispersive estimates for time and space fractional Schrödinger equations. (3rd March 2019)

• Record Type: Journal Article
• Authors: Su, Xiaoyan; Zhao, Shiliang; Li, Miao
• Other Names: Zeidan Dia guestEditor.; Herbst R Sheldon guestEditor.; Lu Tzon‐Tzer guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 10(2021)
• Page Start: 7933
• Page End: 7942
• Publication Date: 2019-03-03
• Subjects: dispersive estimates -- Mittag‐Leffler functions -- time and space fractional Schrödinger equation; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5550
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we consider the Cauchy problem for the fractional Schrödinger equation i D t α u − ( − Δ ) β 2 u = 0 with 0 < α < 1, β > 0. We establish the dispersive estimates by a carefully study of the Mittag‐Leffler functions and give some applications as well. In particular, we prove that the decay rates are sharp.