Abstract
Initial and impulsive conditions for initial value problems of systems of nonlinear impulsive Riemann–Liouville fractional differential equations are introduced. The case when the lower limit of the fractional derivative is changed at each time point of the impulses is studied. In the case studied, the solution has a singularity at the initial time and at any point of the impulses. This leads to the need to appropriately generalize the classical concept of Lipschitz stability. Two derivative types of Lyapunov functions are utilized in order to deduce sufficient conditions for the new stability concept. Three examples are provided for illustration purpose of the theoretical results.
Recommended Citation
M. Bohner and S. Hristova, "Lipschitz Stability for Impulsive Riemann–liouville Fractional Differential Equations," Kragujevac Journal of Mathematics, vol. 48, no. 5, pp. 723 - 745, Faculty of Science, University of Kragujevac, Jan 2024.
The definitive version is available at https://doi.org/10.46793/KgJMat2405.723B
Department(s)
Mathematics and Statistics
Keywords and Phrases
generalized Lipschitz stability in time; Impulses; Lyapunov functions; Riemann–Liouville derivative
International Standard Serial Number (ISSN)
2406-3045; 1450-9628
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2024 Faculty of Science, University of Kragujeva, All rights reserved.
Publication Date
01 Jan 2024
