Geodesic
Lipschitz Stability for Impulsive Riemann--Liouville Fractional Differential Equations
Kragujevac Journal of Mathematics, Tome 48 (2024) no. 5, p. 723 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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.
Classification : 34A08, 34A37, 34K37, 34D20
Keywords: impulses, Riemann–Liouville derivative, generalized Lipschitz stability in time, Lyapunov functions. 
@article{KJM_2024_48_5_a5,
     author = {Martin Bohner and Snezhana Hristova},
     title = {Lipschitz {Stability} for {Impulsive} {Riemann--Liouville} {Fractional} {Differential} {Equations}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {723 },
     year = {2024},
     volume = {48},
     number = {5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2024_48_5_a5/}
}
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Martin Bohner; Snezhana Hristova. Lipschitz Stability for Impulsive Riemann--Liouville Fractional Differential Equations. Kragujevac Journal of Mathematics, Tome 48 (2024) no. 5, p. 723 . http://geodesic.mathdoc.fr/item/KJM_2024_48_5_a5/