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Lyapunov Functions and Lipschitz Stability for Riemann–Liouville Non-Instantaneous Impulsive Fractional Differential Equations
- Source :
- Symmetry, Vol 13, Iss 730, p 730 (2021), Symmetry; Volume 13; Issue 4; Pages: 730
- Publication Year :
- 2021
- Publisher :
- MDPI AG, 2021.
-
Abstract
- In this paper a system of nonlinear Riemann–Liouville fractional differential equations with non-instantaneous impulses is studied. We consider a Riemann–Liouville fractional derivative with a changeable lower limit at each stop point of the action of the impulses. In this case the solution has a singularity at the initial time and any stop time point of the impulses. This leads to an appropriate definition of both the initial condition and the non-instantaneous impulsive conditions. A generalization of the classical Lipschitz stability is defined and studied for the given system. Two types of derivatives of the applied Lyapunov functions among the Riemann–Liouville fractional differential equations with non-instantaneous impulses are applied. Several sufficient conditions for the defined stability are obtained. Some comparison results are obtained. Several examples illustrate the theoretical results.
- Subjects :
- Lyapunov function
Riemann–Liouville fractional derivative
differential equations
non-instantaneous impulses
Lipschitz stability in time
Lyapunov functions
Physics and Astronomy (miscellaneous)
Differential equation
General Mathematics
01 natural sciences
symbols.namesake
Singularity
Computer Science (miscellaneous)
QA1-939
Initial value problem
0101 mathematics
Mathematics
Mathematics::Complex Variables
010102 general mathematics
Mathematical analysis
Lipschitz continuity
Action (physics)
Fractional calculus
010101 applied mathematics
Nonlinear system
Chemistry (miscellaneous)
symbols
Subjects
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 13
- Issue :
- 730
- Database :
- OpenAIRE
- Journal :
- Symmetry
- Accession number :
- edsair.doi.dedup.....22ba541eaf4dedf41fbf34fa8818178f