In order to differentiate photons produced from different origins at hadron colliders, it is necessary to impose some isolation requirements. For cones with small radius , photon isolation effects can be captured by a fragmentation function describing the fragmentation of a parton into a photon accompanied by soft radiation. We computed these fragmentation functions for fixed energy cones and Frixione cones to gain a better understanding of the effects of the isolation parameters on the cross section of . The fragmentation function prediction is compared to the NLO predictions. Finally, we resum the leading logarithms of and of , the ratio of energy inside the cone to the photon energy, and compared it to the measurement performed at ATLAS.