Abstract: With the high speed development of computer science and the increasing ability of calculation, the Fractional Calculus (FC) and Fractional Differential Equations (FDEs) appear more and more frequently in research areas and engineering applications. An easy-to-use and effective method for solving such equations is needed. Though some analytic solutions of FDEs can be resolved, most FDEs do not have exact analytic solutions. So approximation and numerical techniques must be used. In the study, given a set of grid points {xi}, i = 1, 2, …, n and corresponding function values, {f (xi)}, i = 1, 2, …, n, we use two methods to computer the fractional differentiation of function f (x)-Lagrange interpolation polynomial method and Chebyshev polynomial method.