*Accepted Paper*

**Inserted:** 22 dec 2022

**Last Updated:** 15 sep 2023

**Journal:** Advanced Nonlinear Studies

**Year:** 2023

**Doi:** http://dx.doi.org/10.1515/ans-2023-0103

**Abstract:**

This paper deals with existence of solutions to the following fractional
$p$-Laplacian system of equations
\begin{equation**}
%\tag{$\mathcal P$}\label{MAT1}
\begin{cases}
(-\Delta _{p)}^{s} u =**

u

^{{p}^{}

v

v

u

u

^{p^*_s-2}u$ in $\mathbb{R}^N$. For all $\gamma>0$, we establish existence of a positive radial solution to the above system in balls. For $\Omega=\mathbb{R}^N$, we also establish existence of positive radial solutions to the above system in various ranges of $\gamma$.