Approximate controllability of second-order neutral stochastic differential evolution systems with random impulsive effect and state-dependent delay

Chunli You; Linxin Shu; Xiao-bao Shu; Chunli You; Linxin Shu; Xiao-bao Shu

doi:10.3934/math.20241403

AIMS Mathematics

2024, Volume 9, Issue 10: 28906-28930. doi: 10.3934/math.20241403

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Research article

Approximate controllability of second-order neutral stochastic differential evolution systems with random impulsive effect and state-dependent delay

1.
College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang 330063, Jiangxi, China
2.
College of Mathematics, Hunan University, Changsha 410082, Hunan, China

Received: 27 July 2024 Revised: 19 September 2024 Accepted: 25 September 2024 Published: 14 October 2024
MSC : 34F05, 34K45, 34K50

In this paper, we have discussed a class of second-order neutral stochastic differential evolution systems, based on the Wiener process, with random impulses and state-dependent delay. The system is an extension of impulsive stochastic differential equations, since its random effect is not only from stochastic disturbances but also from the random sequence of the impulse occurrence time. By using the cosine operator semigroup theory, stochastic analysis theorem, and the measure of noncompactness, the existence of solutions was obtained. Then, giving appropriate assumptions, the approximate controllability of the considered system was inferred. Finally, two examples were given to illustrate the effectiveness of our work.
- second-order neutral stochastic differential evolution systems,
- random impulses,
- state-dependent delay,
- approximate controllability
Citation: Chunli You, Linxin Shu, Xiao-bao Shu. Approximate controllability of second-order neutral stochastic differential evolution systems with random impulsive effect and state-dependent delay[J]. AIMS Mathematics, 2024, 9(10): 28906-28930. doi: 10.3934/math.20241403

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Abstract

In this paper, we have discussed a class of second-order neutral stochastic differential evolution systems, based on the Wiener process, with random impulses and state-dependent delay. The system is an extension of impulsive stochastic differential equations, since its random effect is not only from stochastic disturbances but also from the random sequence of the impulse occurrence time. By using the cosine operator semigroup theory, stochastic analysis theorem, and the measure of noncompactness, the existence of solutions was obtained. Then, giving appropriate assumptions, the approximate controllability of the considered system was inferred. Finally, two examples were given to illustrate the effectiveness of our work.

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