  We introduce a complex of cochains, $\alpha$-fractional charges ($0 < \alpha
\leq 1$), whose regularity is between that of De Pauw-Moonens-Pfeffer's charges
and that of Whitney's flat cochains. We show that $\alpha$-H\"older
differential forms and their exterior derivative can be realized as
$\alpha$-fractional charges, and that it is possible to define the exterior
product between an $\alpha$-fractional and a $\beta$-fractional charge, under
the condition that $\alpha + \beta > 1$. This construction extends the Young
integral in arbitrary dimension and codimension.
