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

• 论文 • 上一篇    下一篇

STABILITY ANALYSIS OF CAUSAL INTEGRAL EVOLUTION IMPULSIVE SYSTEMS ON TIME SCALES

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

  1. 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. 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: 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