For stochastic evolution equations with fractional derivatives, classical solutions exist when the order of the time derivative of the unknown function is not too small compared to the order of the time derivative of the noise; otherwise, there can be a generalized solution in suitable weighted chaos spaces. Presence of fractional derivatives in both time and space leads to various modifications of the stochastic parabolicity condition. Interesting new effects appear when the order of the time derivative in the noise term is less than or equal to one-half.

中文翻译：

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分数阶随机微分方程的经典解和广义解

对于带有分数导数的随机演化方程，当未知函数的时间导数的阶数与噪声的时间导数的阶数相比不太小时，存在经典解。否则，在合适的加权混沌空间中可以有一个广义的解。分数导数在时间和空间中的存在会导致随机抛物线条件的各种修改。当噪声项中时间导数的阶次小于或等于二分之一时，会出现有趣的新效果。