Existence and stability of mild solutions to non autonomous impulsive stochastic neutral integrodifferential equations

Volume 17, Issue 4, pp 191--207 https://dx.doi.org/10.22436/jnsa.017.04.03

Publication Date: October 04, 2024 Submission Date: January 11, 2023 Revision Date: May 14, 2024 Accteptance Date: July 13, 2024

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Authors

P. A. Thiam - UFR SAT Département de Mathématiques, Université Gaston Berger de Saint-Louis, B.P234, Saint-Louis, Sénégal. Kh. Elbou - Département de Mathématiques et Informatique, Université de Nouakchot A-Lasriya, Mauritania. S. A. Abdi - Département de Mathématiques et Informatique, Université de Nouakchot A-Lasriya, Mauritania. M. A. Diop - UFR SAT Département de Mathématiques, Université Gaston Berger de Saint-Louis, B.P234, Saint-Louis, Sénégal. - c-UMMISCO UMI 209 IRD/UPMC, Bondy, France.

Abstract

‎The research presented in this article focuses on studying a specific category of impulsive stochastic neutral integrodifferential systems in real Hilbert space‎. ‎The first step in this process is to derive sufficient conditions for the existence and uniqueness of a mild solutions‎. ‎We obtain our results using Banach's fixed point theorem and various techniques from stochastic analysis‎. ‎In addition‎, ‎an investigation of the exponential \(p\)-stability of the mild solutions is carried out‎. ‎For an illustration of how our findings can be used‎, ‎see the final section of this paper‎.

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Keywords

• Neutral stochastic integro-differential equations
• resolvent operator
• mild solution
• standard Brownian motion
• exponential stability

MSC

•  47G20
•  47A10
•  49J30
•  60G22
•  03C45

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