‎a spectral collocation method‎ for solving stochastic fractional integro-differential equation

This paper presents a numerical scheme based on shifted vieta-lucas polynomials to solve stochastic fractional integrodifferential equations (sfides). the proposed method approximates brownian motion using gauss-legendre quadrature, simplifying computational processes. additionally, it employs strategically chosen collocation points to transform the target stochastic equation into a system of algebraic equations, which are solved via newtons method. convergence and error analyses of the method are rigorously established. the study further examines the existence and uniqueness of solutions for the considered equations. numerical examples demonstrate the effectiveness, compatibility, and accuracy of the proposed technique, highlighting its advantages in reducing computational effort while maintaining minimal error margins.