Ordinary differential equations
On the orbital Hausdorff dependence of differential equations with non-instantaneous impulses
Comptes Rendus. Mathématique, Volume 356 (2018) no. 2, pp. 150-171.

In this article, we investigate the orbital Hausdorff continuous dependence of the solutions to integer order and fractional nonlinear non-instantaneous differential equations. The concept of orbital Hausdorff continuous dependence is used to characterize the relations of solutions corresponding to the impulsive points and junction points in the sense of the Hausdorff distance. Then, we establish sufficient conditions to guarantee this specific continuous dependence on their respective trajectories. Finally, two examples are given to illustrate our theoretical results.

Nous étudions ici la dépendance orbitale de Hausdorff continue des solutions des équations différentielles d'ordre entier ou fractionnaire, non linéaires avec impulsion non instantanée. Le concept de dépendance orbitale de Hausdorff continue est utilisé pour évaluer la distance de Hausdorff entre les solutions correspondant aux points d'impulsion et de jonction. Nous montrons ensuite des conditions suffisantes garantissant cette dépendance continue spécifique sur leurs trajectoires respectives. Finalement, nous donnons deux exemples qui illustrent nos résultats théoriques.

Accepted:
Published online:
DOI: 10.1016/j.crma.2018.01.001

Dan Yang 1; JinRong Wang 1; Donal O'Regan 2

1 Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, China
2 School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
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Dan Yang; JinRong Wang; Donal O'Regan. On the orbital Hausdorff dependence of differential equations with non-instantaneous impulses. Comptes Rendus. Mathématique, Volume 356 (2018) no. 2, pp. 150-171. doi : 10.1016/j.crma.2018.01.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.01.001/

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Cited by Sources:

The authors acknowledge the National Natural Science Foundation of China (11661016), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006), and Unite Foundation of Guizhou Province ([2015]7640).