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In this paper, we present the analytical solutions, based on the Laplace transform method, for the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations of the photon at the leading order (LO) and next-to-leading order (NLO) approximations in perturbative QCD. Using these solutions, we derive the singlet, non-singlet, gluon, and photon distribution functions of the photon and also the photon structure function F γ 2 (x, Q 2) at the LO and NLO approximations. We show that the resulting distribution functions are in agreement with the results of the parameterization model formulated by Gluck, Reya, and Vogt (GRV) (Phys Rev D 46(5):1973, 1992). Moreover, our numerical results of F γ 2 (x, Q 2) are comparable with the results achieved by

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