Weak solution for fractional $$(p_1,\ldots , p_m)$$(p1,…,pm) -Laplacian system with Dirichlet-type boundary conditions

In the present paper, we prove the existence and uniqueness of weak solutions to a class of fractional $$(p_1,\ldots , p_m)$$ -Laplacian problem with Dirichlet-type boundary conditions, the main tool used here is the variational method combined with the theory of fractional Sobolev spaces.