Application of flatlet oblique multiwavelets to solve the fractional stochastic integro‐differential equation using Galerkin method

Abstract

This study introduces a new numerical approach named flatlet oblique multiwavelets (FOMW) to solve fractional‐order stochastic integro‐differential equation (FSI‐DE). The FOMW is used to create an operational matrix of the stochastic integral, which helps transform the FSI‐DE into a linear system of algebraic equations. This method requires only a small number of basis functions to achieve satisfactory results. The paper also includes a comprehensive discussion on error estimation and convergence analysis, which provides an upper bound of error for the proposed method. Furthermore, numerical experiments have been conducted and compared with other methods, demonstrating the superiority of FOMW in terms of accuracy and efficiency.