# American Institute of Mathematical Sciences

doi: 10.3934/eect.2021001

## Existence results for fractional impulsive delay feedback control systems with Caputo fractional derivatives

 Guangxi University for Nationalities, Faculty of Mathematics and Physics, Nanning 530006, Guangxi Province, P. R. China

* Corresponding author: Biao Zeng

Received  May 2020 Revised  October 2020 Published  January 2021

Fund Project: The first author is supported by the Natural Science Foundation of Guangxi Province grant No. 2019GXNSFBA185005, the Start-up Project of Scientific Research on Introducing talents at school level in Guangxi University for Nationalities grant No. 2019KJQD04 and the Xiangsihu Young Scholars Innovative Research Team of Guangxi University for Nationalities grant No. 2019RSCXSHQN02

The goal of this paper is to provide systematic approaches to study the feedback control systems governed by fractional impulsive delay evolution equations involving Caputo fractional derivatives in separable reflexive Banach spaces. This work is a continuation of previous work. We firstly give an existence result of mild solutions for the equations by applying the Banach's fixed point theorem and the Leray-Schauder alternative fixed point theorem. Next, by using the Filippove theorem and the Cesari property, we obtain the existence result of feasible pairs for the feedback control system. Finally, some applications are given to illustrate our main results.

Citation: Biao Zeng. Existence results for fractional impulsive delay feedback control systems with Caputo fractional derivatives. Evolution Equations & Control Theory, doi: 10.3934/eect.2021001
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