Stability Concepts of Riemann-Liouville Fractional-Order Delay Nonlinear Systems

Ravi Agarwal, Snezhana Hristova and Donal O’Regan
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Ravi Agarwal: Department of Mathematics, Texas A&M University-Kingsville, Kingsville, TX 78363, USA
Snezhana Hristova: Faculty of Mathematics and Informatics, University of Plovdiv “Paisii Hilendarski”, 4000 Plovdiv, Bulgaria
Donal O’Regan: School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, H91 CF50 Galway, Ireland

Mathematics, 2021, vol. 9, issue 4, 1-16

Abstract: First, we set up in an appropriate way the initial value problem for nonlinear delay differential equations with a Riemann-Liouville (RL) fractional derivative. We define stability in time and generalize Mittag-Leffler stability for RL fractional differential equations and we study stability properties by an appropriate modification of the Razumikhin method. Two different types of derivatives of Lyapunov functions are studied: the RL fractional derivative when the argument of the Lyapunov function is any solution of the studied problem and a special type of Dini fractional derivative among the studied problem.

Keywords: Riemann-Liouville fractional derivative; time-varying delay; stability; Lyapunov functions; fractional derivatives of Lyapunov functions; Razumikhin method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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