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Stability Analysis of Causal Integral Evolution Impulsive Systems on Time Scales

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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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, China

    Jiafa Xu  (徐家发)

  2. Department of Mathematics, University of Peshawar, Peshawar, 25000, Pakistan

    Bakhtawar Pervaiz & Akbar Zada

  3. Department of Physical and Numerical Sciences, Qurtuba University of Science and Information Technology Peshawar, Dera Ismail Khan, Pakistan

    Syed Omar Shah

Authors
  1. Jiafa Xu  (徐家发)
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  2. Bakhtawar Pervaiz
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  3. Akbar Zada
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  4. Syed Omar Shah
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Corresponding author

Correspondence to Jiafa Xu  (徐家发).

Additional information

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).

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Xu, J., Pervaiz, B., Zada, A. et al. Stability Analysis of Causal Integral Evolution Impulsive Systems on Time Scales. Acta Math Sci 41, 781–800 (2021). https://doi.org/10.1007/s10473-021-0310-2

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  • DOI: https://doi.org/10.1007/s10473-021-0310-2

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