In this paper, we are concerned with existence, uniqueness and numerical approximation of the solution process to an initial value problem for stochastic fractional differential equation of Riemann-Liouville type. We propose and analyze a Petrov-Galerkin finite element method based on fractional (non-polynomial) Jacobi polyfractonomials as basis and test functions. Error estimates in $L^2$ norm are derived and numerical experiments are provided to validate the theoretical results. As an illustrative application, we generate sample paths of the Riemann-Liouville fractional Brownian motion which is of importance in many applications ranging from geophysics to traffic flow in telecommunication networks.

在本文中，我们关注 Riemann-Liouville 型随机分数阶微分方程初值问题求解过程的存在性、唯一性和数值近似。我们提出并分析了基于分数（非多项式）雅可比多项式作为基础和测试函数的 Petrov-Galerkin 有限元方法。误差估计在${升}^2$推导出范数，并提供数值实验来验证理论结果。作为说明性应用，我们生成了黎曼-刘维尔分数布朗运动的样本路径，这在从地球物理学到电信网络中的交通流的许多应用中都很重要。