One of the challenging and practical issues that have recently attracted the attention of researchers is stochastic equations. One of the important categories in stochastic equations is the stochastic fractional integro-differential equations (SFIDEs), which are practical tools for modeling many phenomena. In this study, we aim to derive a novel numerical method based on the meshless enhanced moving least squares (EMLS) and spectral method for solving SFIDEs, which transform the intended problem to a nonlinear system of algebraic equations. Thus, the complexity of solving the mentioned problem is reduced significantly. Also, we give an error estimate which will be useful in estimating the error of approximate solutions for the problems that we do not have information about their exact solutions. Illustrative numerical examples are also given to clarify the performance and accuracy of the new method. This method is far from computational complexity compared to other methods. Also, obtaining acceptable accuracy by choosing a small number of interpolation nodes and basis functions is one of the innovations of this work.
