Matrix Order Differintegration
Abstract
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.
Cite
@article{arxiv.math-ph/0312051,
title = {Matrix Order Differintegration},
author = {Mark Naber},
journal= {arXiv preprint arXiv:math-ph/0312051},
year = {2007}
}
Comments
Presented at the 78 th annual meeting of the Michigan Section of the Mathematical Association of America and MichMATYC at Lawrence Technological University, Southfield MI, May 10-11, 2002