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Stability of Ulam–Hyers and Existence of Solutions for Impulsive Time-Delay Semi-Linear Systems with Non-Permutable Matrices

Author

Listed:
  • Nazim I. Mahmudov

    (Department of Mathematics, Eastern Mediterranean University, Famagusta 99628, T.R. North Cyprus Mersin 10, Turkey)

  • Amal M. Almatarneh

    (Department of Mathematics, Eastern Mediterranean University, Famagusta 99628, T.R. North Cyprus Mersin 10, Turkey)

Abstract

In this paper, the stability of Ulam–Hyers and existence of solutions for semi-linear time-delay systems with linear impulsive conditions are studied. The linear parts of the impulsive systems are defined by non-permutable matrices. To obtain solution for linear impulsive delay systems with non-permutable matrices in explicit form, a new concept of impulsive delayed matrix exponential is introduced. Using the representation formula and norm estimation of the impulsive delayed matrix exponential, sufficient conditions for stability of Ulam–Hyers and existence of solutions are obtained.

Suggested Citation

  • Nazim I. Mahmudov & Amal M. Almatarneh, 2020. "Stability of Ulam–Hyers and Existence of Solutions for Impulsive Time-Delay Semi-Linear Systems with Non-Permutable Matrices," Mathematics, MDPI, vol. 8(9), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1493-:d:408369
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