Abstract
In this paper, we are concerned with some qualitative properties of the new fractional Musielak–Sobolev spaces such that the generalized Poincaré type inequality and some continuous and compact embedding results. Moreover, we prove that any function in may be extended to a function in , with is a bounded domain of class . In addition, we establish a result that relates to the complemented subspace in . As an application, using the mountain pass theorem and some variational methods, we investigate the existence of a nontrivial weak solution for a class of nonlocal fractional type problems with Dirichlet boundary data.
Disclosure statement
No potential conflict of interest was reported by the author(s).