This paper studied the fractional calculus, given three types of numerical methods of solving fractional differential equations, that is the Fractional Euler method, The Fractional Backward differential method(BDF method) and the Fractional Order Reduced Backward differential method(FORBDF method). The numerical results show that these methods are effective, and we discussed the application of the fractional calculus to the viscoelastic material problem. Finally, the paper made a summary of the major work and prospected for future work