Motivated by fractional derivative models in viscoelasticity, a class of semilinear stochastic Volterra integro-differential equations, and their deterministic counterparts, are considered. A generalized exponential Euler method, named here as the Mittag-Leffler Euler integrator, is used for the temporal discretization, while the spatial discretization is performed by the spectral Galerkin method. The temporal rate of strong convergence is found to be (almost) twice compared to when the backward Euler method is used together with a convolution quadrature for time discretization. Numerical experiments that validate the theory are presented.

中文翻译：

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带有加性噪声的随机分数阶方程的 Mittag-Leffler Euler 积分器

受粘弹性中的分数阶导数模型的启发，考虑了一类半线性随机 Volterra 积分微分方程及其确定性对应方程。广义指数欧拉方法（此处称为 Mittag-Leffler Euler 积分器）用于时间离散化，而空间离散化由谱伽辽金方法执行。与后向欧拉方法与卷积正交用于时间离散化时相比，强收敛的时间速率被发现（几乎）两倍。给出了验证该理论的数值实验。