On density of smooth functions in weighted fractional Sobolev spaces

We prove that smooth $C^\infty$ functions are dense in weighted fractional Sobolev spaces on an arbitrary open set, under some mild conditions the weight. also obtain a~similar result non-weighted defined by kernel similar to $x\mapsto |x|^{-d-sp}$. One may consider results be a~version of Meyers--Serrin theorem.