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On the Inverse of the Caputo Matrix Exponential
- Source :
- Mathematics, Vol 7, Iss 12, p 1137 (2019)
- Publication Year :
- 2019
- Publisher :
- MDPI AG, 2019.
-
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.
- Subjects :
- caputo matrix exponential
matrix inverse
fractional derivative
Mathematics
QA1-939
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 7
- Issue :
- 12
- Database :
- Directory of Open Access Journals
- Journal :
- Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.008dfd6339a142ccbc8bc99cf5013099
- Document Type :
- article
- Full Text :
- https://doi.org/10.3390/math7121137