  The linearization of a quadratic form gives rise to a Clifford algebra
structure, as seen in Dirac's factorization of the d'Alembert operator. A
similar structure known as a generalized Clifford algebra arises from the
continuation of this procedure to higher order forms. This technique combined
with the existence of a fractional derivative satisfying the semi-group
property can be used to factor the d'Alembert operator further, producing a
fractional partial differential matrix equation that has a similar form to
Dirac's equation. We examine these equations, their solutions, and point out
difficulties when attempting to make physical sense of them.
