Differential inclusion systems with fractional competing operator and multivalued fractional convection term

In this work, the existence of solutions (in a suitable sense) to a family of inclusion systems involving fractional, possibly competing, elliptic operators, fractional convection, and homogeneous Dirichlet boundary conditions is established. The technical approach exploits Galerkin's method and a surjective results for multifunctions in finite dimensional spaces as well as approximating techniques.