Liouville theorems for fractional elliptic systems with different orders

Abstract In this paper, we establish some new Liouville‐type theorems for nonnegative weak solutions to fractional elliptic systems with different orders. To prove our result, we will use the local realization of fractional Laplacian, which can be constructed as Dirichlet‐to‐Neumann operator of a degenerate elliptic equation by the extension technique. Our proof is based on Alexandrov–Serrin method of moving planes based on some maximum principles that obtained by establishing some key integral inequalities.