  Properties of the phase space of the standard map with memory are
investigated. This map was obtained from a kicked fractional differential
equation. Depending on the value of the parameter of the map and the fractional
order of the derivative in the original differential equation this nonlinear
dynamical system demonstrates attractors (fixed points, stables periodic
trajectories, slow converging and slow diverging trajectories, ballistic
trajectories, and fractal-like structures) and/or chaotic trajectories. At
least one type of fractal-like sticky attractors in the chaotic sea was
observed.
