Well-posedness and Mittag-Leffler Euler integrator for space-time fractional SPDEs with fractionally integrated additive noise

@article{Dai2022WellposednessAM,
  title={Well-posedness and Mittag-Leffler Euler integrator for space-time fractional SPDEs with fractionally integrated additive noise},
  author={Xinjie Dai and Jialin Hong and Derui Sheng},
  journal={ArXiv},
  year={2022},
  volume={abs/2206.00320}
}
This paper considers the space-time fractional stochastic partial differential equation (SPDE, for short) with fractionally integrated additive noise, which is general and includes many (fractional) SPDEs with additive noise. Firstly, the existence, uniqueness and temporal regularity of the mild solution are presented. Then the Mittag–Leffler Euler integrator is proposed as a time-stepping method to numerically solve the underlying model. Two key ingredients are developed to overcome the… 
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