  In this work, using the Laplace transformation technique we present our
results for non-singlet quark distributions as well as nucleon structure
function $F_2(x,Q^2)$ in unpolarized case at next-to-next-to-leading order
(NNLO) QCD accuracy. We shall particularly compare our results for the sets of
valence-quark parton distribution functions with the contemporary
collaborations like CT14, CT18, MMHT14, MKAM16 and NNPDF. To construct the
nucleon structure function we employ the expansion of Jacobi polynomials which
is a suitable transform to convert the results of non-singlet structure
function from the Laplace $s$-space to Bjorken $x$-space. We shall also
consider the contributions of target mass correction as well as the higher
twist effects at large-$x$ region for the proton and deuteron structure
functions. Our results for the unpolarized quark distribution functions and
nucleon structure functions are in good agreement with recent theoretical
models and available experimental data.
