Fractional type multivariate neural network operators

Kadak U.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.46, no.3, pp.3045-3065, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 3
  • Publication Date: 2023
  • Doi Number: 10.1002/mma.7460
  • 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.3045-3065
  • Keywords: Data modeling, fractional calculus, multivariate neural network, neurocomputing process, order of approximation
  • Gazi University Affiliated: Yes

Abstract

In this paper, we introduce a novel family of multivariate neural network operators involving Riemann-Liouville fractional integral operator of order alpha. Their pointwise and uniform approximation results are presented, and new results concerning the rate of convergence in terms of the modulus of continuity are estimated. Moreover, several graphical and numerical results are presented to demonstrate the accuracy, applicability, and efficiency of the operators through special activation functions. Finally, an illustrative real-world example on the recent trend of novel corona virus Covid-19 has been investigated in order to demonstrate the modeling capabilities of the proposed neural network operators.