Recent Progress on Stochastic Fractional Diffusion Equations with Space-Time White Noise

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Abstract

We review the recent development on stochastic fractional diffusion equations with space-time white noise. We explicate the Fox $H$-function, fundamental solutions, mild Skorohod solution and its properties including existence and uniqueness, intermittent property and Hölder continuity.

Keywords:

Stochastic partial differential equation space-time white noise Fox $H$-function intermittency Hölder continuity

Author Biographies

  • Yuhui Guo

    Guangdong Provincial Key Laboratory of IRADS, Department of Mathematical Sciences, Beijing Normal – Hong Kong Baptist University, Zhuhai 519087, China

  • Jiang-Lun Wu

    Guangdong Provincial Key Laboratory of IRADS, Department of Mathematical Sciences, Beijing Normal – Hong Kong Baptist University, Zhuhai 519087, China

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DOI

10.4208/cmaa.2025-0019