  A next-to-next-to-leading order (NNLO) QCD calculation of gluon distribution
function at small-x is presented. The gluon distribution function is explored
analytically in the DGLAP approach by a Taylor expansion at small x as two
first order partial differential equations in two variables : Bjorken x and t
(t = ln(Q2/{\Lambda}2) ). We have solved the system of equations at LO, NLO and
NNLO respectively by the La- granges method. The resulting analytical
expressions are compared with the available global PDF sets as well as with the
results of the BDM model. We have further performed a \c{hi}2 test to check the
com- patibility of our predictions and observed that our results can be
consistently described in the context of perturbative QCD. A comparative
analysis of the obtained results at LO, NLO and NNLO reveals that the NNLO
approximation has a significant contribution to the gluon distribution function
particularly in the small-x region.
