Numerical Solution of Stochastic Fractional Integro-Differential Equations: The Poly-sinc Collocation Approach

This paper presents a polynomial sinc-based collocation method, combined with Gauss–Legendre/Newton–Cotes quadrature rules, to solve stochastic fractional integro-differential equations (SFIDEs). The method approximates the solution by applying Lagrangian polynomial interpolation at sinc collocation points and simplifies the SFIDE into a system of algebraic equations, requiring low/moderate computational efforts. The proposed method is also accompanied by an error analysis, and numerical examples are provided to demonstrate its efficiency and accuracy. In noiseless conditions, the method achieves spectral accuracy and behaves like other conventional sinc methods. Finally, the paper simulates an application of a class of these equations.