Approximate controllability for a class of fractional semilinear system with instantaneous and non-instantaneous impulses

Yunhao Chu; Yansheng Liu; Yunhao Chu; Yansheng Liu

doi:10.3934/mmc.2024022

Mathematical Modelling and Control

2024, Volume 4, Issue 3: 273-285. doi: 10.3934/mmc.2024022

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Approximate controllability for a class of fractional semilinear system with instantaneous and non-instantaneous impulses

Yunhao Chu ,
Yansheng Liu ^,

School of Mathematics and Statistics, Shandong Normal University, Ji'nan 250014, China

Received: 03 February 2023 Revised: 25 July 2024 Accepted: 17 August 2023 Published: 28 August 2024

This paper is mainly concerned with the existence of mild solutions and approximate controllability for a class of fractional semilinear systems with instantaneous and non-instantaneous impulses. By applying the Kuratowski measure of noncompactness and $ \rho $-set contractive fixed-point theorem, the results for the considered system were obtained. In the end, an example was studied to support the main results.
Citation: Yunhao Chu, Yansheng Liu. Approximate controllability for a class of fractional semilinear system with instantaneous and non-instantaneous impulses[J]. Mathematical Modelling and Control, 2024, 4(3): 273-285. doi: 10.3934/mmc.2024022

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Abstract

This paper is mainly concerned with the existence of mild solutions and approximate controllability for a class of fractional semilinear systems with instantaneous and non-instantaneous impulses. By applying the Kuratowski measure of noncompactness and $ \rho $-set contractive fixed-point theorem, the results for the considered system were obtained. In the end, an example was studied to support the main results.

References

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