Fractional order logistic map: Numerical approach

In this paper the fractional order logistic map in sense of Caputo's differences is numerically approached. It shown that necessary iterations number to avoid transients must be thousand, not hundreds as commonly used several works. Also, it revealed an interesting phenomenon according which for every initial condition correspond a different bifurcation diagram. This seems appear also other FO difference systems, fact could represent obstacle numerical analysis. A short Matlab code obtain results.