Density properties for fractional Musielak-Sobolev spaces

TL;DR

This paper introduces a new fractional Musielak-Sobolev space and investigates the density of smooth, compactly supported functions within it, expanding the functional analysis framework for variable exponent spaces.

Contribution

The paper defines a novel fractional Musielak-Sobolev space and establishes key density properties of smooth functions in this setting.

Findings

Density of smooth functions in the new space is proven.

The space generalizes classical fractional Sobolev spaces.

Results facilitate further analysis in variable exponent fractional spaces.

Abstract

In this paper, we introduce a new fractional Musielak-Sobolev space $Ws,{\Phi}x,y({\Omega})$ where ${\Omega}$ is an open subset in RN and we show some density properties of smooth and compactly supported functions in this space.