Principal curves to fractional $m$-Laplacian systems and related maximum and comparison principles

In this paper we develop a comprehensive study on principal eigenvalues and both the (weak and strong) maximum and comparison principles related to an important class of nonlinear systems involving fractional $m$-Laplacian operators. Explicit lower bounds for principal eigenvalues of this system in terms of the diameter of $\mathrm{\Omega }$ are also proved. As application, given $\lambda ,\mu \ge 0$ we measure explicitly how small has to be $\text{diam}(\mathrm{\Omega })$ so that weak and strong maximum principles associated to this problem hold in $\mathrm{\Omega }$.