Abstract

The aim of this work is to study the stability for some integro-differential equations with impulses driven by fractional Brownian motion with noncompact semigroup in Hilbert spaces. We assume that the linear part has a resolvent operator not necessary compact but is operator norm continuous. Sufficient conditions for the existence of mild solutions are obtained using the Hausdorff measure of noncompactness and the Mönch fixed point theorem. Further, we establish a new impulsive-integral inequality to prove the exponential stability of mild solutions in the mean square moment. Finally, an example is presented to illustrate our obtained results.

Details

Title
Stability for some impulsive neutral stochastic functional integro-differential equations driven by fractional Brownian motion
Author
Diop, Mamadou Abdoul 1   VIAFID ORCID Logo  ; Khalil Ezzinbi 2 ; Louk-Man Issaka 2 ; Kasinathan Ramkumar 3 

1  UFR SAT Département De Mathématiques, Université Gaston Berger De Saint-Louis, Saint-Louis B.P234, Sénégal 
2  Département De Mathématiques, Faculté Des Sciences Semlalia, Université Cadi Ayyad, Marrakech B.P 2390, Morocco 
3  Department of Mathematics, PSG College of Arts and Science, Coimbatore 641 014, India 
Publication year
2020
Publication date
Jan 2020
Publisher
Taylor & Francis Ltd.
e-ISSN
25742558
Source type
Scholarly Journal
Language of publication
English
DOI
https://doi.org/10.1080/25742558.2020.1782120
ProQuest document ID
3218424012
Copyright
© 2020 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license. This work is licensed under the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.