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Applicable Analysis
An International Journal
Volume 103, 2024 - Issue 2
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Research Article

Existence and approximate controllability results for second-order impulsive stochastic neutral differential systems

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Pages 481-505 | Received 05 Oct 2021, Accepted 23 Mar 2023, Published online: 29 Mar 2023
 

Abstract

This paper focuses on the existence and approximate controllability of second-order non-autonomous impulsive stochastic neutral differential systems in Hilbert spaces. First, by using Schauder's fixed-point theorem, stochastic analysis theory, and evolution operators, a new set of sufficient conditions are formulated, and we prove the existence of mild solutions of second-order non-autonomous impulsive stochastic neutral differential systems. Further, the result is extended to study the approximate controllability results for second-order non-autonomous impulsive stochastic neutral differential systems. Then, a set of sufficient conditions are derived for the approximate controllability of second-order non-autonomous impulsive stochastic neutral differential system by assuming the associated linear system is approximately controllable. The results are obtained with the help of Krasnoselskii's fixed point theorem. Finally, an example is given to illustrate our obtained results.

2020 Mathematics Subject Classifications:

Disclosure statement

No potential conflict of interest was reported by the author(s).

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