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Predictions of fiducial cross sections, differential cross sections andlepton charge asymmetry are presented for the production of $W^{\pm}$ bosonswith leptonic decay up to next-to-next-to-leading order (NNLO) in perturbativeQCD. Differential cross sections of $W^{\pm}$ bosons and W boson lepton chargeasymmetry are computed as a function of lepton pseudorapidity for a definedfiducial region in $pp$ collisions at $\sqrt{s}=13$ TeV. Numerical results offiducial $W^{\pm}$ cross section predictions are presented with the latestmodern PDF models at next-to-leading order (NLO) and NNLO. It is found that theCT14 and NNPDF 3.0 predictions with NNLO QCD corrections are about 4$\%$ higherthan the NLO CT14 and NNPDF 3.0 predictions while MMHT 2014 predictions withNLO QCD corrections are smaller than its NNLO QCD predictions by approximately6$\%$. In addition, the NNLO QCD corrections reduce the scale variationuncertainty on the cross section by a factor of 3.5. The prediction of centralvalues and considered uncertainties are obtained using FEWZ 3.1 program.

High order QCD predictions for inclusive production of $W$ bosons in $pp$ collisions at $\sqrt{s}$$=13$ TeV