A bipolynomial fractional Dirichlet-Laplace problem

In the paper, we derive an existence result for a nonlinear nonautonomous partial elliptic system on an open bounded domain with Dirichlet boundary conditions, containg fractional powers of the weak Dirichlet-Laplace operator that are meant in the Stone-von Neumann operator calculus sense. We apply a variational method which gives strong solutions of the problem under consideration.