A remark on the qualitative conditions of nonlinear IDEs


Tunç C.

INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, vol.15, no.3, pp.905-922, 2020 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 3
  • Publication Date: 2020
  • Journal Name: INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.905-922
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this paper, the stability (S), asymptotic stability (AS), uniform stability (US) of null solution and boundedness of solutions of non-linear Volterra integro-differential equations (IDEs) are investigated by means of the Lyapunov-Krasovskii method (LKM). Four new theorems are provided on the mentioned concepts for the considered (IDEs). Compared with past related results in the literature, our conditions are simple, weaker and convenient for testing and applications. The obtained results also improve and extend the past related results. Finally, two numerical examples are provided to illustrate the applications of our results.