On analytical solutions of the DIS structure functions in the framework of GLR-MQ-ZRS equation

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.