  This work further develops the properties of fractional differential forms.
In particular, finite dimensional subspaces of fractional form spaces are
considered. An inner product, Hodge dual, and covariant derivative are defined.
Coordinate transformation rules for integral order forms are also computed.
Matrix order fractional calculus is used to define matrix order forms. This is
achieved by combining matrix order derivatives with exterior derivatives.
Coordinate transformation rules and covariant derivative for matrix order forms
are also produced. The Poincare' lemma is shown to be true for exterior
fractional differintegrals of all orders excluding those whose orders are
non-diagonalizable matrices.
