FAPT: a Mathematica package for calculations in QCD Fractional Analytic Perturbation Theory

We provide here all the procedures in $\mathtt{\text{Mathematica}}$ which are needed for the computation of the analytic images of the strong coupling constant powers in Minkowski (${\bar{\mathfrak{A}}}_{\nu }(s;n_f)$ and ${\mathfrak A_{\nu}^$\text{glob}$(s)}$)andEuclidean(${\bar{\mathcal A}{\nu}(Q^2;n_f)}$and${\mathcal A{\nu}^$\text{glob}$(Q^2)}$) domains at arbitrary energy scales ($s$ and $Q^2$, correspondingly) for both schemes — with fixed number of active flavours $n_f=3,4,5,6$ 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 and its generalization — Fractional APT, needed to apply the APT imperative for renormalization-group improved hadronic observables.