  In this paper, we derive analytic expressions for coefficients of the
equations that allow calculations of asymptotically periodic points in
fractional difference maps. Numerical solution of these equations allows us to
draw the bifurcation diagram for the fractional difference logistic map. Based
on the numerically calculated bifurcation points, we make a conjecture that in
fractional maps the value of the Feigenbaum constant $\delta$ is the same as in
regular maps, $\delta=4.669...$.
