The time fractional Schrödinger equation with a nonlinearity of Hartree type

JOURNAL OF EVOLUTION EQUATIONS（2021）

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摘要

The aim of this work is to show existence, uniqueness and regularity properties of local in time mild solutions for the nonlinear space-time fractional Schrödinger equation ( 1.1 ), with a fractional time derivative of order α∈ (0,1), and with a nonlinear term of Hartree type.

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关键词

Time fractional Schrodinger equation, Caputo fractional derivative, Fractional Laplace operator, Fractional-order Sobolev space, Hartree-type nonlinearity

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