Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (3): 781-800.doi: 10.1007/s10473-021-0310-2

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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).

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

CLC Number: 

  • 34N05
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