Functions of bounded higher variation in the fractional Sobolev spaces

In this paper, we establish fine properties of functions of bounded higher variation in the framework of fractional Sobolev spaces. In particular, inspired by the recent work of Brezis-Nguyen on the distributional Jacobian, we extend the definition of functions of bounded higher variation, which defined by Jerrard-Soner in W-1,W- N-1 boolean AND L-infinity(Omega, R-N), to the fractional Sobolev space W-1-1(/N,) N (Omega, R-N), and apply Cartesian currents theory to establishing general versions of coarea formula, chain rule and decomposition property.