  In this paper, the shape of the stability domain S^q for a class of
difference systems defined by the Caputo forward difference operator D^q of
order q\in (0, 1) is numerically analyzed. It is shown numerically that due to
of power of the negative base in the expression of the stability domain, in
addition to the known cardioid-like shapes, S^q could present supplementary
regions where the stability is not verified. The Mandelbrot map of fractional
order is considered as an illustrative example. In addition, it is conjectured
that for $q < 0.5$, the shape of S^q does not cover the main body of the
underlying Mandelbrot set of fractional order as in the case of integer order.
