Blow-up phenomena for porous medium equation driven by the fractional $ p $-sub-Laplacian

In this paper, we investigate the global existence and blow-up phenomena of the solution to the fractional nonlinear porous medium equation on stratified groups, employing the concavity method. Specifically, we establish the necessary conditions for the existence of global solutions and blow-up solutions. Our findings not only contribute to the understanding of this equation on stratified groups but also extend the existing knowledge in the classical Euclidean setting to the fractional case.