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In this talk,I will report our group’s work on the finite difference methods for the time fractional order differential equations.The outline is as follows.· Approximations to the fractional derivatives · Finite difference methods for the fractional sub-diffusion equation · Finite difference methods for the fractional diffusion-wave equation · Finite difference methods for the multi-term fractional diffusion-wave equation · ADI methods for the multi-dimensional fractional equations.