Abstract
This manuscript is devoted to the numerical solutions of coupled system of fractional partial differential equations (FPDEs). Using Legendre polynomials for two variables, we developed some operational matrices. Based on these matrices the considered coupled system is converted to some algebraic equations which can be easily solved for the unknown coefficient matrices needed in the approximate solutions of u(x, t), v(x, t). The established technique is then applied to some numerical examples and the results are compared with some known wavelet methods, which demonstrate that our proposed method provides excellent solutions as compared to the other numerical methods.