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<p>The present work investigates the local well-posedness of the Cauchy problem for a class of time-space fractional nonlinear Schrödinger equation with a generalized Riesz potential or with a classical Bessel potential. The main methods to prove the existence and uniqueness of the local-in-time mild solution on a fractional Sobolev space are based upon the Banach fixed-point theorem and some powerful tools in harmonic analysis.</p>

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On a class of time-space fractional nonlinear Schrödinger equation with the Riesz potential or Bessel potential

  • 期刊论文

  • 发表日期：

    2025年12月10日

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  • Sen Wang,
  • Xian-Feng Zhou,
  • Jia-Bao Liu,
  • Denghao Pang,
  • Biao Liu

摘要

The present work investigates the local well-posedness of the Cauchy problem for a class of time-space fractional nonlinear Schrödinger equation with a generalized Riesz potential or with a classical Bessel potential. The main methods to prove the existence and uniqueness of the local-in-time mild solution on a fractional Sobolev space are based upon the Banach fixed-point theorem and some powerful tools in harmonic analysis.