Abstract:In the paper, we apply a numerical approach to approximate solution of a system of the fractional differential equations based on the Müntz-Legendre polynomials.Features of these polynomials make them so appropriate for solving the fractional differential equation system. In the proposed method, a system of the fractional differential equations is transformed into a system of the algebraic equations which is move easier to solve. The numerical examples show accuracy and convergence of the present method.