The time fractional Schrödinger equation with a nonlinearity of Hartree type

Abstract

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 \(\alpha \in (0,1),\) and with a nonlinear term of Hartree type.

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Acknowledgements

H.P. has been partially supported by FONDECYT grant #1170571.

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Correspondence to Humberto Prado.

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Prado, H., Ramírez, J. The time fractional Schrödinger equation with a nonlinearity of Hartree type. J. Evol. Equ. (2021). https://doi.org/10.1007/s00028-020-00658-y

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Keywords

  • Time fractional Schrödinger equation
  • Caputo fractional derivative
  • Fractional Laplace operator
  • Fractional-order Sobolev space
  • Hartree-type nonlinearity

Mathematics Subject Classification

  • Primary: 34K37
  • 35R11
  • 46E35
  • Secondary: 37L05
  • 35S05