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 Uniqueness and Existence of solutions for a singular system with nonlocal operator via perturbation method Kamel Saoudi,Mouna Kratou,Eadah AlZahrani Keywords:Singular nonlocal elliptic system, approximated methods, variationals methods, existence of solutions, uniqueness of solutions. Abstract: In this work, we investigate the existence and the uniqueness of solutions for the nonlocal elliptic system involving a singular nonlinearity as follows: \begin{eqnarray*} \left\{\begin{array}{ll} (-\Delta_p)^su = a(x)|u|^{q-2}u +\frac{1-\alpha}{2-\alpha-\beta} c(x)|u|^{-\alpha}|v|^{1-\beta}, \quad \text{in }\Omega,\ \ (-\Delta_p)^s v= b(x)|v|^{q-2}v +\frac{1-\beta}{2-\alpha-\beta} c(x)|u|^{1-\alpha}|v|^{-\beta}, \quad \text{in }\Omega,\ \ u=v = 0 ,\;\;\mbox{ in }\,\mathbb{R}^N\setminus\Omega, \end{array} \right. \end{eqnarray*} where $\Omega$ is a bounded domain in $R^{n}$ with smooth boundary, $0<\alpha <1,$ $0<\beta <1,$ \$2-\alpha -\beta