Finite-Time Stability of a Class of Nonstationary Nonlinear Fractional Order Time Delay Systems: New Gronwall–Bellman Inequality Approach

Mihailo P. Lazarević (), Stjepko Pišl and Darko Radojević
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Mihailo P. Lazarević: Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia
Stjepko Pišl: Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Belgrade, Serbia
Darko Radojević: SC “Pinki-Zemun”, Gradski Park 2, Zemun, 11080 Beograd, Serbia

Mathematics, 2025, vol. 13, issue 9, 1-17

Abstract: This paper aims to analyze finite-time stability (FTS) for a class of nonstationary nonlinear two-term fractional-order time-delay systems with α , β ∈ 0 , 2 . Using a new type of generalized Gronwall–Bellman inequality, we derive new FTS stability criteria for these systems in terms of the Mittag–Leffler function. We demonstrate that our theoretical results are less conservative than those presented in the existing literature. Finally, we provide three numerical examples using a modified Adams–Bashforth–Moulton algorithm to illustrate the applicability of the proposed stability conditions.

Keywords: finite-time stability; convergence analysis; fractional order; time delay; nonlinear system; new Gronwall–Bellman inequality; numerical solving of integral equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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