On the qualitative analyses solutions of new mathematical models of integro-differential equations with infinite delay

Tunç C., Tunç O., Wen C., Yao J.

Mathematical Methods in the Applied Sciences, vol.46, no.13, pp.14087-14103, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 13
  • Publication Date: 2023
  • Doi Number: 10.1002/mma.9306
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.14087-14103
  • Keywords: boundedness, GUAS, instability, integrability, nonlinear IDEs, US
  • Van Yüzüncü Yıl University Affiliated: Yes


This paper deals with the uniformly stability (US), globally uniformly asymptotically stability (GUAS) and instability of zero solution as well as integrability and boundedness of nonzero solutions of certain nonlinear integro-differential equations (IDEs). We prove five new theorems, which include sufficient conditions related to these fundamental qualitative properties of solutions to the IDEs considered. The main tools used in the proof are two new and suitable Lyapunov–Krasovskiiˇ functionals (LKFs). In particular cases, two numerical examples are given and solved via the fourth order Runge–Kutta method (RKM) in MATLAB to illustrate the theoretical results of this paper. Compared with the existing results on the fundamental qualitative behaviors of scalar IDEs, our results are new, original, more effective and convenient for tests and applications.