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

Shah, Syed; Tunç, Cemil; Rizwan, Rizwan; Zada, Akbar; Khan, Qayyum; Ullah, Iftikhar; Ullah, Ibrar

doi:10.1007/s12346-022-00639-1

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

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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)

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.