On the Fundamental Analyses of Solutions to Nonlinear Integro-Differential Equations of the Second Order


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Tunç C., Tunç O.

Mathematics, vol.10, no.22, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 22
  • Publication Date: 2022
  • Doi Number: 10.3390/math10224235
  • Journal Name: Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: boundedness, first order, global asymptotic stability, infinite delay, integrability, integro-differential equation, integro-differential system, LKF, second order
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

© 2022 by the authors.In this article, a scalar nonlinear integro-differential equation of second order and a non-linear system of integro-differential equations with infinite delays are considered. Qualitative properties of solutions called the global asymptotic stability, integrability and boundedness of solutions of the second-order scalar nonlinear integro-differential equation and the nonlinear system of nonlinear integro-differential equations with infinite delays are discussed. In the article, new explicit qualitative conditions are presented for solutions of both the second-order scalar nonlinear integro-differential equations with infinite delay and the nonlinear system of integro-differential equations with infinite delay. The proofs of the main results of the article are based on two new Lyapunov–Krasovskiĭ functionals. In particular cases, the results of the article are illustrated with three numerical examples, and connections to known tests are discussed. The main novelty and originality of this article are that the considered integro-differential equation and system of integro-differential equations with infinite delays are new mathematical models, the main six qualitative results given are also new.