The effect of nonperturbative and higher order perturbative corrections to the free nucleon structure
functions in the deep inelastic scattering (DIS) of neutrinos on the free nucleon/nuclear target is studied. The evaluation of the nucleon structure functions have been performed up to next-to-next-to-leading order (NNLO) by
using the Martin$-$Motylinski$-$Harland$-$Lang$-$Thorne 2014 parametrization of the parton distribution
functions. The various nucleon and nuclear effects considered in this work are effective in the
different regions of x and $Q^2$, and quite important in the few GeV energy region.
The numerical calculations for the $\nu-A$ DIS process have been
performed by incorporating the nuclear medium effects like Fermi motion, binding energy, nucleon correlations, mesonic contributions, shadowing, and antishadowing in several nuclear targets such as carbon, polystyrene scintillator, argon, iron and lead
which are being used in MINERvA, ArgoNeuT and DUNE experiments.