A new class of fractional Orlicz-Sobolev space and singular elliptic problems

Abstract

This paper seeks to introduce a new class of fractional Orlicz-Sobolev space with variable-order. We give basic properties of this space and prove some compactness results. Then, using some techniques of calculus of variations combined with theory of Musielak functions, we prove the existence of a nonnegative weak solution for a singular elliptic type problem in a fractional variable-order Orlicz-Sobolev space with homogeneous Dirichlet boundary conditions.