Title

A dynamic matrix exponential via a matrix cylinder transformation

Document Type

Article

Publication Title

Journal of Mathematical Analysis and Applications

Abstract

In this work, we develop a new matrix exponential on time scales via a cylinder transformation with a component-wise, locally μΔ-integrable square matrix subscript. Our resulting matrix function can be written in terms of the matrix exponential of a Lebesgue integral added to a logarithmic sum in terms of the gaps of a general time scale. Under strict commutativity conditions, we show our dynamic matrix exponential is equivalent to the one in the standard literature. Finally, we demonstrate that our matrix exponential satisfies a nonlinear dynamic integral equation.

DOI

https://doi.org/10.1016/j.jmaa.2019.06.048

Publication Date

11-2019

Creative Commons License

Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.

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