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In this paper, the differential cross section of charmed mesons production (   $$D_{s}^{\pm }$$  D s ± ,    $$D^{0}$$  D 0 ,    $$D^{*}$$  D ∗ and    $$D^{*\pm }$$  D ∗ ± and    $$D^{\pm }$$  D ± ) are computed as a function of transverse momentum    $$p_{T}$$  p T and the total cross sections. The hadronization mechanism is considered via a fragmentation process of a  c  heavy quark to a light-heavy meson according to Suzuki’s model. The two-cutoff phase-space slicing method has been applied to calculate the phase-space integral of two- and three-body subprocess cross sections and fragmentation function (FF) at next-to-leading order (NLO) accuracy. By using Monte Carlo (MC) techniques, we try to properly estimate the ratio of neutral to charged  D -meson production    $$R_{u/d}$$  R u / d and the strangeness-suppression factor    $$\gamma _{s}$$  γ s . Our numerical results show that the NLO corrections of the FF have significant effect on  D -mesons production and enhance the cross section ratio at NLO respect to leading order (LO) about    $$50\%$$  50 % . A comparison indicates that our cross section results are in agreement (within uncertainties) with available data from ATLAS and ALICE and theoretical predictions of the fixed-order next-to-leading-logarithm (FONLL) approach and NLO parton-shower MC simulation (MC@NLO) in high-energy proton–proton (pp) collisions at    $$\sqrt{s}=7TeV$$  s = 7 T e V .

Cross section of D-mesons production via the c-quark fragmentation process at next-to-leading order accuracy in pp collisions at the 7TeV LHC