We analytically solved the QED ⊗ QCD-coupled DGLAP evolution equations at leading 15 order (LO) quantum electrodynamics (QED) and next-to-leading order (NLO) quantum 16 chromodynamics (QCD) approximations, using the Laplace transform method and then 17 computed the proton structure function in terms of the unpolarized parton distribution 18 functions. Our analytical solutions for parton densities are in good agreement with those from CT14QED (1.2952 < Q2 < 1010 19 ) (Ref. 6) global parametrizations and APFEL (A PDF Evolution Library) (2 < Q2 < 108 20 ) (Ref. 4). We also compared the proton structure function, F2p(x, Q^2 ), with the experimental data released by the ZEUS and H1 22 collaborations at HERA. There is a nice agreement between them in the range of low and high x and Q^2 .

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