Derivatives and integrals: matrix order operators as an extension of the fractional calculus
arXiv:2005.00091
Abstract
A natural consequence of the fractional calculus is its extension to a matrix order of differentiation and integration. A matrix-order derivative definition and a matrix-order integration arise from the generalization of the gamma function applied to the fractional differintegration definition. This work focuses on some results applied to the Riemann-Liouville version of the fractional calculus extended to its matrix-order concept. This extension also may apply to other versions of fractional calculus. Some examples of possible ordinary and partial matrix-order differential equations and related exact solutions are shown.
This article presents some properties of matrix order calculus, including exact solutions for differential equations. The numerical treatment will be published in a future article