In this work, we provide the first strong convergence result of numerical approximation of a general second order semilinear stochastic fractional order evolution equation involving a Caputo derivative in time of order $\alpha\in(\frac 12, 1)$ and driven by Gaussian and non-Gaussian noises simultaneously more useful in concrete applications. The Gaussian noise considered here is a Hilbert space valued Q-Wiener process and the non-Gaussian noise is defined through compensated Poisson random measure associated to a L\'evy process. The linear operator is not necessary self-adjoint. The fractional stochastic partial differential equation is discretized in space by the finite element method and in time by a variant of the exponential integrator scheme. We investigate the mean square error estimate of our fully discrete scheme and the result shows how the convergence orders depend on the regularity of the initial data and the power of the fractional derivative.

翻译：在这项工作中,我们提供了第二个总顺序半线性分序进化方程式的数值近似的第一个强烈趋同结果,该方程式在时间顺序为$\alpha\in(frac 12,1美元)时涉及卡普托衍生物,由高森和非高森噪音驱动,同时在混凝土应用中更为有用。这里所考虑的高森噪音是一个Hilbert空间,其价值为Q-Wiierer过程,而非加西南噪音则通过与L\'evy过程相关的补偿性Poisson随机措施加以定义。线性操作器没有必要自相连接。分解的分解性部分偏差方程式通过有限元素方法在空间中分离,并及时通过指数化集成体办法的变式分离。我们调查了我们完全离散的系统的平均平方差估计值,其结果显示趋同顺序取决于初始数据的规律性和分数衍生物的功率。