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Dispersive estimates for time and space fractional Schrödinger equations
Author(s) -
Su Xiaoyan,
Zhao Shiliang,
Li Miao
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5550
Subject(s) - mathematics , initial value problem , fractional calculus , cauchy problem , space (punctuation) , mathematical analysis , cauchy distribution , schrödinger equation , mittag leffler function , mathematical physics , linguistics , philosophy
In this paper, we consider the Cauchy problem for the fractional Schrödinger equation i D t α u − ( − Δ )β 2u = 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.