Stability of Ulam-Hyers and existence of solutions for impulsive time-delay semi-linear systems with non-permutable matrices

Mahmudov N., Almatarneh A. M.

Mathematics, vol.8, no.9, 2020 (SCI-Expanded, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 8 Say: 9
  • Nəşr tarixi: 2020
  • Doi nömrəsi: 10.3390/math8091493
  • jurnalın adı: Mathematics
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Açar sözlər: Delayed matrix exponential, Impulsive delay equation, Stability
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

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.