Existence of weak solutions for fractional elliptic problems involving double phase operators

In this paper, we study a class of fractional singular elliptic problems driven by the double phase operator with a gradient-dependent reaction term under Dirichlet boundary conditions. By applying topological degree theory for discontinuous operators through the abstract Hammerstein equation framework, we establish the existence of weak solutions in fractional Musielak–Orlicz–Sobolev spaces. The assumptions employed are new and more general than those available in the existing literature. Consequently, our results extend and complement several previous works concerning nonlocal singular double phase problems.