Pion form factor in QCD sum rules, local duality approach, and O(A_2) fractional analytic perturbation theory

Using the results on the electromagnetic pion Form Factor (FF) obtained in the $O({\alpha }_s)$ QCD sum rules with non-local condensates \cite{BPS09} we determine the effective continuum threshold for the local duality approach. Then we apply it to construct the $O({\alpha }_s^2)$ estimation of the pion FF in the framework of the fractional analytic perturbation theory.