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

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