Damghan University Press Analytical and Numerical Solutions for Nonlinear Equations 3060-785X 6 2 2021 11 01 Shifted Legendre Tau Method for Solving the Fractional Stochastic Integro-Differential Equations 221 241 224 10.22128/gadm.2021.491.1065 EN Ruhangiz Azimi Associate Professor, Mathematics and Computer Science Department, Adib mazandaran institute of higher education, Sari, Iran 0000-0003-4926-6830 Mostafa Mohagheghy Nezhad Associate Professor,Mathematica and Computer Science Department, Adib mazandaran institute of higher education, Sari, Iran 0000-0001-8529-0673 Saedeh Foadian School of Mathematics and Computer Science, Damghan University, Damghan, Iran 0000-0001-7091-1254 Journal Article 2022 01 13 ‎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 Ito-integration 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. https://ansne.du.ac.ir/article_224_cfd90650de4bbf92864047c9ca1defd8.pdf