On the singular elliptic problem involving the variable order fractional Musielak $g_{x,y}$-Laplacian

In this paper, we investigate the existence of positive weak solutions to a nonlocal singular elliptic problem under Dirichlet boundary condition. Problem is settled in fractional Musielak-Sobolev spaces with variable order. The main tool is variational approach, however, various auxiliary tools from the theory of nonlinear functional analysis, convex analysis and critical point theory are also applied.