This work is an extended version of the ICCS 2020 conference paper [1]. The paper aims to present an efficient numerical method to quantify the uncertainty in the solution of stochastic fractional integro-differential equations. The numerical method presented here is a wavelet collocation method based on Legendre polynomials, and their deterministic and stochastic operational matrix of integration. The operational matrices are used to convert the stochastic fractional integro-differential equation to a linear system of algebraic equations. The accuracy and efficiency of the proposed method are validated through numerical experiments. Moreover, the results are compared with the numerical methods based on the Gaussian radial basis function (GA RBF) and thin plate splines radial basis function (TBS RBF) to show the superiority of the proposed method. Finally, concerning the real-world application, a stock market model has been simulated and the results are demonstrated.

这项工作是ICCS 2020会议论文[1]的扩展版本。本文旨在提供一种有效的数值方法来量化随机分数阶积分微分方程解的不确定性。这里提出的数值方法是一种基于勒让德多项式的小波配置方法，以及它们的确定性和随机积分运算矩阵。运算矩阵用于将随机分数积分微分方程转换为代数方程的线性系统。通过数值实验验证了该方法的准确性和有效性。此外，将结果与基于高斯径向基函数（GA RBF）和薄板花键径向基函数（TBS RBF）的数值方法进行了比较，证明了该方法的优越性。