New Fundamental Results on the Continuous and Discrete Integro-Differential Equations

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Tunç O., Tunç C., Yao J., Wen C.

MATHEMATICS, vol.10, no.9, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 9
  • Publication Date: 2022
  • Doi Number: 10.3390/math10091377
  • 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: nonlinear system of IDEs, stability, instability, integrability, boundedness at infinity, LKF, DIFFERENTIAL-EQUATIONS, STABILITY PROPERTIES, BOUNDEDNESS, SYSTEM
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

This work studies certain perturbed and un-perturbed nonlinear systems of continuous and discrete integro-delay differential equations (IDDEs). Using the Lyapunov-Krasovskii functional (LKF) method and the Lyapunov-Razumikhin method (LRM), uniform asymptotic stability (UAS), uniform stability (US), integrability and boundedness of solutions as well as exponential stability (ES) and instability of solutions are discussed. In this paper, five new theorems and a corollary are given and three numerical applications are provided with their simulations. With this work, we aim to make new contributions to the theory of the continuous and discrete integro-differential equations.