Shifted Legendre Tau Method for Solving the Fractional Stochastic Integro-Differential Equations

‎In this paper‎, ‎the Tau method based on shifted Legendre polynomials is proposed for solving a class of fractional stochastic integro-differential equations‎. ‎For this purpose‎, ‎shifted Legendre polynomials and their properties are introduced‎. ‎By using the operational matrices of integration and stochastic Itointegration we transform the problem into the corresponding linear system of algebraic equations‎. ‎Finally the efficiency of the proposed method is confirmed by some examples‎. ‎The results show that this method is very accurate and efficient‎.