Perturbative QCD fitting of KEDR and BESIII $e^+e^-$ data for R(s) and $\alpha_s$ determination

The experimental data collected by KEDR and BESIII collaborations at the energies below charm quark thresholds are compared with the QCD expressions for the $e^+e^-$ annihilation R-ratio truncated at different orders of perturbation theory. The fits demonstrate the dependence of the extracted $\alpha_s(M_Z)$ values from orders of the truncation of the corresponding approximations. The next-to-leading order, next-to-next-to-leading order and next-to-next-to-next-to-leading order fits of the combined KEDR data and BESIII data , truncated at the mass scale of $J/\Psi$ meson, give the following results $\alpha_s(M_Z)= 0.1179^{+0.0051}_{-0.0069}$,$\alpha_s(M_Z)=0.1221^{+0.0063}_{-0.0080}$ and $\alpha_s(M_Z)=0.1312^{+0.0027}_{-0.0067}$. The subjects related to the applications of the fixed orders of perturbation theory expansions and careful treatment of the analytical continuation effects are commented.