FAPT: a Mathematica package for calculations in QCD Fractional Analytic Perturbation Theory. We provide here all the procedures in Mathematica which are needed for the computation of the analytic images of the strong coupling constant powers in Minkowski (¯Aν (s; nf ) and Aglob ν (s)) and Euclidean ( ¯Aν (Q2; nf ) and Aglob ν (Q2)) domains at arbitrary energy scales (s and Q2, correspondingly) for both schemes — with fixed number of active flavours nf = 3, 4, 5, 6 and the global one with taking into account all heavy-quark thresholds. These singularity-free couplings are inevitable elements of Analytic Perturbation Theory (APT) in QCD, proposed in [10,69,70], and its generalization — Fractional APT, suggested in [42,46,43], needed to apply the APT imperative for renormalization-group improved hadronic observables.