1. Stability Concepts of Riemann-Liouville Fractional-Order Delay Nonlinear Systems.
- Author
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Agarwal, Ravi, Hristova, Snezhana, O'Regan, Donal, and Goodrich, Christopher
- Subjects
- *
NONLINEAR differential equations , *NONLINEAR systems , *DELAY differential equations , *FRACTIONAL differential equations , *LYAPUNOV functions , *INITIAL value problems - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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