Local absorbing boundary conditions (LABCs) for nonlinear Schrödinger equations have been constructed in papers [PRE 78 (2008) 026709; and PRE 79 (2009) 046711] using the so-called unified approach.

In this paper, two ADI schemes are developed for solving the two-dimensional time fractional nonlinear super-diffusion equations based on their equivalent partial integrodifferential equations.