Bielecki-Ulam's Types Stability Analysis of Hammerstein and Mixed Integro-Dynamic Systems of Non-Linear Form with Instantaneous Impulses on Time Scales


Shah S. O., Tunç C., Rizwan R., Zada A., Khan Q. U., Ullah I., ...More

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, vol.21, no.4, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 4
  • Publication Date: 2022
  • Doi Number: 10.1007/s12346-022-00639-1
  • Journal Name: QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Keywords: Bielecki-Ulam-Hyers stability, Impulses, Time scale, Dynamic system, ALMOST-PERIODIC SOLUTIONS, DIFFERENTIAL-EQUATIONS, EXISTENCE, MODEL, BOUNDEDNESS, UNIQUENESS
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this paper, the stability in terms of Bielecki-Ulam-Hyers and stability in terms of Bielecki-Ulam-Hyers-Rassias of non-linear impulsive Hammerstein integro-dynamic system with delay and non-linear impulsive mixed integro-dynamic system on time scales are achieved by utilizing fixed point approach along with Lipschitz condition and Gronwall's inequality. Examples are also provided for the verification of the results.