STABILITY ANALYSIS OF CAUSAL INTEGRAL EVOLUTION IMPULSIVE SYSTEMS ON TIME SCALES

doi:10.1007/s10473-021-0310-2

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (3): 781-800.doi: 10.1007/s10473-021-0310-2

STABILITY ANALYSIS OF CAUSAL INTEGRAL EVOLUTION IMPULSIVE SYSTEMS ON TIME SCALES

徐家发¹, Bakhtawar PERVAIZ², Akbar ZADA², Syed Omar SHAH³

1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China;
2. Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan;
3. Department of Physical and Numerical Sciences, Qurtuba University of Science and Information Technology Peshawar, Dera Ismail Khan, Pakistan

收稿日期:2019-12-05 修回日期:2020-07-22 出版日期:2021-06-25 发布日期:2021-06-07
通讯作者: Jiafa XU E-mail:xujiafa292@sina.com
作者简介:Bakhtawar PERVAIZ,E-mail:Bakhtawar@uop.edu.pk; Akbar ZADA,E-mail:zadababo@yahoo.com;Syed Omar SHAH,E-mail:omarshah89@yahoo.com
基金资助:
The first author is supported by Talent Project of Chongqing Normal University (02030307-0040), the China Posdoctoral Science Foundation (2019M652348), Natural Science Foundation of Chongqing (cstc2020jcyj-msxmX0123), and Technology Research Foundation of Chongqing Educational Committee (KJQN202000528, KJQN201900539).

STABILITY ANALYSIS OF CAUSAL INTEGRAL EVOLUTION IMPULSIVE SYSTEMS ON TIME SCALES

Jiafa XU¹, Bakhtawar PERVAIZ², Akbar ZADA², Syed Omar SHAH³

1. School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China;
2. Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan;
3. Department of Physical and Numerical Sciences, Qurtuba University of Science and Information Technology Peshawar, Dera Ismail Khan, Pakistan

Received:2019-12-05 Revised:2020-07-22 Online:2021-06-25 Published:2021-06-07
Contact: Jiafa XU E-mail:xujiafa292@sina.com
About author:Bakhtawar PERVAIZ,E-mail:Bakhtawar@uop.edu.pk; Akbar ZADA,E-mail:zadababo@yahoo.com;Syed Omar SHAH,E-mail:omarshah89@yahoo.com
Supported by:
The first author is supported by Talent Project of Chongqing Normal University (02030307-0040), the China Posdoctoral Science Foundation (2019M652348), Natural Science Foundation of Chongqing (cstc2020jcyj-msxmX0123), and Technology Research Foundation of Chongqing Educational Committee (KJQN202000528, KJQN201900539).

摘要/Abstract

摘要： In this article, we present the existence, uniqueness, Ulam-Hyers stability and Ulam-Hyers-Rassias stability of semilinear nonautonomous integral causal evolution impulsive integro-delay dynamic systems on time scales, with the help of a fixed point approach. We use Grönwall's inequality on time scales, an abstract Gröwall's lemma and a Picard operator as basic tools to develop our main results. To overcome some difficulties, we make a variety of assumptions. At the end an example is given to demonstrate the validity of our main theoretical results.

关键词: Time scale, Ulam-Hyers stability, impulses, semilinear nonautonomous system, Gr?nwall's inequality, dynamic system

Abstract: In this article, we present the existence, uniqueness, Ulam-Hyers stability and Ulam-Hyers-Rassias stability of semilinear nonautonomous integral causal evolution impulsive integro-delay dynamic systems on time scales, with the help of a fixed point approach. We use Grönwall's inequality on time scales, an abstract Gröwall's lemma and a Picard operator as basic tools to develop our main results. To overcome some difficulties, we make a variety of assumptions. At the end an example is given to demonstrate the validity of our main theoretical results.

Key words: Time scale, Ulam-Hyers stability, impulses, semilinear nonautonomous system, Gr?nwall's inequality, dynamic system

中图分类号:

34N05

徐家发, Bakhtawar PERVAIZ, Akbar ZADA, Syed Omar SHAH. STABILITY ANALYSIS OF CAUSAL INTEGRAL EVOLUTION IMPULSIVE SYSTEMS ON TIME SCALES[J]. 数学物理学报(英文版), 2021, 41(3): 781-800.

Jiafa XU, Bakhtawar PERVAIZ, Akbar ZADA, Syed Omar SHAH. STABILITY ANALYSIS OF CAUSAL INTEGRAL EVOLUTION IMPULSIVE SYSTEMS ON TIME SCALES[J]. Acta mathematica scientia,Series B, 2021, 41(3): 781-800.

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STABILITY ANALYSIS OF CAUSAL INTEGRAL EVOLUTION IMPULSIVE SYSTEMS ON TIME SCALES

STABILITY ANALYSIS OF CAUSAL INTEGRAL EVOLUTION IMPULSIVE SYSTEMS ON TIME SCALES

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