In this paper, finite difference schemes for differential equations with both temporal and spatial fractional derivatives are studied. When the order of the time fractional derivative is in (Formula presented.) , an alternating direction implicit (ADI) scheme with second-order accuracy in both space and time is constructed. For equations with time fractional derivatives of order lying in (Formula presented.) , a scheme is derived and solved by the generalized minimal residual method. We also propose a preconditioner to improve the efficiency for the implementation of the scheme in this situation.