An alternating direction implicit (ADI) fractional trapezoidal rule (FTR) type difference scheme is formulated and analysed for a two-dimensional fractional evolution equation. In this method, standard central difference approximation used for the spatial discretization and the time stepping – an ADI scheme based on FTR, combined with chosen second-order fractional quadrature rule suggested by Lubich, are considered. TheL2,H1-stability and convergence are derived. Numerical experiments in total agreement with our analysis are reported. [ABSTRACT FROM AUTHOR]