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Open AccessArticle

On the Inverse of the Caputo Matrix Exponential

1
Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain
2
Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019-0408, USA
3
Instituto de Instrumentación para Imagen Molecular, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1137; https://doi.org/10.3390/math7121137
Received: 1 October 2019 / Revised: 14 November 2019 / Accepted: 18 November 2019 / Published: 21 November 2019
(This article belongs to the Section Mathematics and Computer Science)
Matrix exponentials are widely used to efficiently tackle systems of linear differential equations. To be able to solve systems of fractional differential equations, the Caputo matrix exponential of the index α > 0 was introduced. It generalizes and adapts the conventional matrix exponential to systems of fractional differential equations with constant coefficients. This paper analyzes the most significant properties of the Caputo matrix exponential, in particular those related to its inverse. Several numerical test examples are discussed throughout this exposition in order to outline our approach. Moreover, we demonstrate that the inverse of a Caputo matrix exponential in general is not another Caputo matrix exponential. View Full-Text
Keywords: Caputo matrix exponential; matrix inverse; fractional derivative Caputo matrix exponential; matrix inverse; fractional derivative
MDPI and ACS Style

Defez, E.; Tung, M.M.; Chen-Charpentier, B.M.; Alonso, J.M. On the Inverse of the Caputo Matrix Exponential. Mathematics 2019, 7, 1137.

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