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Accessible Unlicensed Requires Authentication Published by De Gruyter May 9, 2020

New finite-time stability analysis of singular fractional differential equations with time-varying delay

Nguyen T. Thanh, Vu N. Phat and Piyapong Niamsup


The Lyapunov function method is a powerful tool to stability analysis of functional differential equations. However, this method is not effectively applied for fractional differential equations with delay, since the constructing Lyapunov-Krasovskii function and calculating its fractional derivative are still difficult. In this paper, to overcome this difficulty we propose an analytical approach, which is based on the Laplace transform and “inf-sup” method, to study finite-time stability of singular fractional differential equations with interval time-varying delay. Based on the proposed approach, new delay-dependent sufficient conditions such that the system is regular, impulse-free and finite-time stable are developed in terms of a tractable linear matrix inequality and the Mittag-Leffler function. A numerical example is given to illustrate the application of the proposed stability conditions.


This work was completed while the first and second authors were visiting the Vietnam Institute for Advanced Study in Mathematics (VIASM). We thank the Institute for its support and hospitality. The research of the first and second authors is supported by NAFOSTED, Vietnam [101.01-2017.300]; the research of the third author is supported by the Chiang Mai University, Thailand. The authors are grateful to the Editor-in-Chief and anonymous reviewers for their valuable comments to improve the paper. We also thank Dr. H.T. Tuan for helpful discussions and suggestions related to Lemma 2.6.


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Received: 2018-05-14
Revised: 2020-03-15
Published Online: 2020-05-09
Published in Print: 2020-04-28

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