Fractional APT in QCD in the Euclidean and Minkowski regions

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We describe the development of Analytic Perturbation Theory (APT) in QCD, called Fractional APT (FAPT), which has been suggested to apply the renormalization group evolution and QCD factorization technique in the framework of APT.
Talk at the International Conference ``New Trends in High-Energy Physics (experiment, phenomenology, theory)'', Yalta, Crimea, Ukraine, Sept. 15--22, 2007; 8pages, 5 figures; Added references

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