The nonlinear time-fractional stochastic fourth-order reaction–diffusion equation perturbed by noises is considered by the mixed finite element method in this paper. Based on the mixed finite element in spatial direction and the generalized BDF$2-\theta$ in temporal discretization, the semi- and fully-discrete schemes are obtained. Further, the error estimates for the semi- and fully-discretizations and the regularity of solution are derived by some important lemmas. The numerical experiment is conducted to further confirm the theoretical results.

中文翻译：

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非线性时间分数阶随机四阶反应扩散方程的混合有限元方法

本文采用混合有限元方法考虑了非线性扰动的时间分数阶随机四阶反应扩散方程。基于空间方向上的混合有限元和广义BDF$2-\theta$在时间离散化中，获得了半离散和全离散方案。此外，半离散和完全离散的误差估计以及解的正则性是由一些重要引理导出的。进行数值实验以进一步证实理论结果。