The Lambert function method in qualitative analysis of fractional delay differential equations

We discuss an analytical method for qualitative investigations of linear fractional delay differential equations. This method originates from the Lambert function technique that is traditionally used in stability analysis of ordinary delay differential equations. Contrary to the existing results based on such a technique, we show that the method can result into fully explicit stability criteria for a linear fractional delay differential equation, supported by a precise description of its asymptotics. As a by-product of our investigations, we also state alternate proofs of some classical assertions that are given in a more lucid form compared to the existing proofs.

Keywords

Fractional delay differential equation (primary), Lambert function, Stability, Asymptotic behavior

Citation

Fractional Calculus and Applied Analysis. 2023, vol. 26, issue 4, p. 1545-1565.
https://link.springer.com/article/10.1007/s13540-023-00176-x

Document type

Peer-reviewed

Document version

Published version

Language of document

en

Document licence

Creative Commons Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/