An application of Lyapunov functions to properties of solutions of a perturbed fractional differential system

Tunç C.

INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE, vol.17, no.2, pp.537-550, 2022 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 2
  • Publication Date: 2022
  • Journal Name: INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.537-550
  • Keywords: Fractional differential system, uniform stability, asymptotic stability, Mittag-Leffer stability, boundedness at infinity, Lyapunov function, Caputo derivative, INTEGRODIFFERENTIAL EQUATIONS, STABILITY ANALYSIS, BOUNDEDNESS
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

This paper deals with a perturbed nonlinear system of fractional order differential equations (FrODEs) with Caputo derivative. The purpose of the paper is to discuss uniform stability (US), asymptotic stability (AS), Mittag-Leffer stability (MLS) of zero solution and boundedness at infinity of non-zero solutions of this perturbed nonlinear system of FrODEs with Caputo derivative. We obtain four new theorems on these mathematical concepts via a Lyapunov function (LF) and its Caputo derivative. For illustration, an example is provided which satisfies assumptions of the four new results and, in particular, shows their applications. The new results of this paper generalize and improve some recent ones in the literature and they have contributions to theory of FrODEs.