The main purpose of this paper is to develop a new method based on operational matrices of the linear cardinal B-spline (LCB-S) functions to numerically solve of the fractional stochastic integro-differential (FSI-D) equations. To reach this aim, LCB-S functions are introduced and their properties are considered, briefly. Then, the operational matrices based on LCB-S functions are constructed, for the first time, including the fractional Riemann-Liouville integral operational matrix, the stochastic integral operational matrix, and the integer integral operational matrix. The main characteristic of the new scheme is to convert the FSI-D equation into a linear system of algebraic equations which can be easily solved by applying a suitable method. Also, the convergence analysis and error estimate of the proposed method are studied and an upper bound of error is obtained. Numerical experiments are provided to show the potential and efficiency of the new method. Finally, some numerical results, for various values of perturbation in the parameters of the main problem are presented which can indicate the stability of the suggested method.

本文的主要目的是开发一种基于线性基数B样条（LCB-S）函数的运算矩阵的新方法，以数值方式求解分数阶随机积分-微分（FSI-D）方程。为了达到这个目的，简要介绍了LCB-S功能并考虑了它们的特性。然后，首次构造了基于LCB-S函数的运算矩阵，包括分数Riemann-Liouville积分运算矩阵，随机积分运算矩阵和整数积分运算矩阵。新方案的主要特征是将FSI-D方程转换为代数方程的线性系统，可以通过应用适当的方法轻松解决。还，对所提方法的收敛性分析和误差估计进行了研究，并获得了误差的上限。数值实验表明了该方法的潜力和有效性。最后，针对主要问题参数的各种摄动值，给出了一些数值结果，这些结果可以表明所提出方法的稳定性。