  We computed the deep inelastic scattering (DIS) structure functions $F_2
(x,Q^2)$ and $F_L (x,Q^2)$ in the framework of Gribov-Levin-Ryskin-Mueller-Qiu,
Zhu-Ruan-Shen (GLR-MQ-ZRS) equation. Both $x$ and $Q^2$ evolutions of the
structure functions are studied in the kinematic range of $10^{-6}\leq x \leq
10^{-2}$ and $5 \leq Q^2 \leq 100\,,GeV^2$ respectively. we have suggested
analytical solutions to the structure functions, our results are inspired by
Regge like behaviour of gluons at small-x. The solutions of structure functions
are obtained for two particular cases: (i) treating the strong coupling
constant $\alpha_s$ as an arbitrary constant, and (ii) considering the $Q^2$
dependency of $\alpha_s$. Our predicted results are in good agreement with the
latest available high precision HERA data.
