Matrix Order Differintegration

Details Matrix Order Differintegration Matrix Order Differintegration

2003-12-19

arxiv.org/abs/math-ph/0312051v1

Physics

Mathematical Physics

Presented at the 78 th annual meeting of the Michigan Section of the Mathematical Association of America and MichMATYC at Lawr

Scientific paper

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.

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