The present work is devoted to study the high-energy QCD events, such as the di-jet productions from proton–proton inelastic collisions at the LHC in the forward-center and the forward-forward configurations. This provides us with much valuable case study, since such phenomena can provide a direct glimpse into the partonic behavior of a hadron in a dominant gluonic region. We use the unintegrated parton distribution functions (UPDF) in the kt-factorization framework. The UPDF of Kimber et al. (KMR) and Martin et al. (MRW) are generated in the leading order (LO) and next-to-leading order (NLO), using the Harland-Lang et al. (MMHT2014) PDF libraries. While working in the forward-center and the forward-forward rapidity sectors, one can probe the parton densities at very low longitudinal momentum fractions (x). Such a model computation can provide simpler analytic description of data with respect to existing formalisms such as perturbative QCD. The differential cross-section calculations are performed at the center of mass energy of 7 TeV corresponding to CMS collaboration measurement. It is shown that the gluonic jet productions are dominant and a good description of data as well as other theoretical attempts (i.e. KS-linear, KS-nonlinear and rcBK) is obtained. The uncertainty of the calculations is derived by manipulating the hard scale of the processes by a factor of two. This conclusion is achieved, due to the particular visualization of the angular ordering constraint (AOC), that is incorporated in the definition of these UPDF.