Mittag-Leffler stability of neural networks with Caputo-Hadamard fractional derivative

DEMİRCİ E., KARAKOÇ F., Kutahyalioglu A.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.47, no.12, pp.10091-10100, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 47 Issue: 12
  • Publication Date: 2024
  • Doi Number: 10.1002/mma.10111
  • 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.10091-10100
  • Keywords: Caputo–Hadamard derivative, Hopfield-type neural networks, Lyapunov function, Mittag-Leffler stability
  • Ankara University Affiliated: Yes

Abstract

In this paper, a Hopfield-type neural network system with Caputo-Hadamard fractional derivative is discussed. The importance of the existence of the equilibrium point in the analysis of artificial neural networks is well known. Another important investigation is the stability properties. So, the stability of a neural network system is dealt with in the present paper. First, a theorem that asserts the existence and uniqueness of the equilibrium point of the system is proven. Later, the conditions that ensure the Mittag-Leffler stability of the equilibrium point is obtained by using the Lyapunov's direct method. In addition, an example is given with numerical simulations to show the effectiveness of our theoretical results.