We consider the light cone sum-rule description of the pion-photon transition form factor, based on dispersion relations, in combination with the renormalization group of QCD, in terms of the formal solution of the Efremov-Radyushkin-Brodsky-Lepage evolution equation, and show that the emerging scheme amounts to a certain version of fractional analytic perturbation theory (FAPT). In order to ensure the correct asymptotic behavior of the considered physical quantity, this modified FAPT version has to be supplemented by process-specific boundary conditions-in contrast to the standard one. However, it provides the advantage of significantly improving the inclusion of radiative corrections in the low-momentum regime of QCD perturbation theory using renormalization-group summation.