A new generalized fractional musielak-sobolev spaces and its applications

This paper investigates a novel class of generalized fractional Musielak-Sobolev spaces denoted by H^s/2;Ψ ξ ,yφ H ϕ s / 2 ; Ψ ξ , y . Key properties such as separability and reflexivity are analyzed in detail. Furthermore, continuous and compact embeddings are rigorously established, together with additional functional-analytic properties. As an application, the framework is used to study the existence and multiplicity of solutions to a class of nonlocal generalized problems, focusing in particular on the nonlocal Schrödinger problem with discontinuous nonlinearity.