CONTROLLABILITY AND HYERS—ULAM STABILITY OF IMPULSIVE SECOND ORDER ABSTRACT DAMPED DIFFERENTIAL SYSTEMS

Akbar Zada; Luqman Alam; Jiafa Xu; Wei Dong

doi:10.11948/20200059

2021 Volume 11 Issue 3

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Akbar Zada, Luqman Alam, Jiafa Xu, Wei Dong. CONTROLLABILITY AND HYERS—ULAM STABILITY OF IMPULSIVE SECOND ORDER ABSTRACT DAMPED DIFFERENTIAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2021, 11(3): 1222-1239. doi: 10.11948/20200059

Citation:

Akbar Zada, Luqman Alam, Jiafa Xu, Wei Dong. CONTROLLABILITY AND HYERS—ULAM STABILITY OF IMPULSIVE SECOND ORDER ABSTRACT DAMPED DIFFERENTIAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2021, 11(3): 1222-1239. doi: 10.11948/20200059

CONTROLLABILITY AND HYERS—ULAM STABILITY OF IMPULSIVE SECOND ORDER ABSTRACT DAMPED DIFFERENTIAL SYSTEMS

1.
Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan
2.
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China
3.
Hebei University of Engineering, Handan, Hebei 056021, China

Author Bio: Email address: zadababo@yahoo.com (A. Zada); Email address: luqmanalam1234@gmail.com (L. Alam); Email address: dongweihd@163.com (W. Dong)
Fund Project: The authors were supported by the National Natural Science Foundation of China(No. 11371117), the China Postdoctoral Science Foundation (No. 2019M652348), Natural Science Foundation of Chongqing (Grant No. cstc2020jcyj-msxmX0123), Technology Research Foundation of Chongqing Educational Committee(No. KJQN202000528, KJQN201900539), the open project of key laboratory (No. CSSXKFKTM202003), School of Mathematical Sciences, Chongqing Normal University

Abstract

Abstract

In this paper, we consider system of damped second order abstract impulsive differential equations to investigate its controllability and Hyers—Ulam stability. For our results about the controllability, we utilized the theory of strongly continuous cosine families of linear operators combined with Sadovskii fixed point theorem. In addition, different types of Hyers—Ulam stability is established with the help of Gr?nwall's type inequality and Lipschitz conditions. At last, we give an example of damped wave equation which outline the application of our principle results.
- Damped differential equation; impulsive system /
- controllability /
- β—Hyers—Ulam—Rassias stability
MSC: 26A33, 34A08, 34B27

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References

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