On the Inverse of the Caputo Matrix Exponential

Emilio Defez, Michael M. Tung, Benito M. Chen-Charpentier and José M. Alonso
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Emilio Defez: Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain
Michael M. Tung: Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain
Benito M. Chen-Charpentier: Department of Mathematics, University of Texas at Arlington, Arlington, TX 76019-0408, USA
José M. Alonso: Instituto de Instrumentación para Imagen Molecular, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain

Mathematics, 2019, vol. 7, issue 12, 1-11

Abstract: 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.

Keywords: Caputo matrix exponential; matrix inverse; fractional derivative (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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