  The Riemann-Liouville formula for fractional derivatives and integrals
(differintegration) is used to derive formulae for matrix order derivatives and
integrals. That is, the parameter for integration and differentiation is
allowed to assume matrix values. It is found that the computation of
derivatives and integrals to matrix order is well defined for any square matrix
over the complex numbers. Some properties are worked out for special classes of
matrices. It is hoped that this new formalism will be of use in the study of
systems of fractional differential equations and sequential fractional
differential equations.
