Application of non-local and non-singular kernel to an epidemiological model with fractional order

Dokuyucu M. A., Dutta H., Yildirim C.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.44, no.5, pp.3468-3484, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 5
  • Publication Date: 2021
  • Doi Number: 10.1002/mma.6954
  • 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.3468-3484
  • Ondokuz Mayıs University Affiliated: No

Abstract

In this century when computers and other electronic devices have taken over the world, the rate at which malwares including viruses are infecting these devices has also started to increase rapidly. The developments of computer systems and its ever increasing uses require preventing strategies of malwares. This study aims to analyze an epidemiological model on the spread of computer viruses. We investigated the existence and uniqueness of solutions, examined the stability of the model, and performed numerical simulations. First, a model has been extended with the help of Atangana-Baleanu fractional derivative in Caputo sense. Then, the fixed point approach has been adopted to investigate the existence and uniqueness of solution of the model. Furthermore, the stability of the model has been examined with the help of the Hyers-Ulam stability method, and the model's numerical solutions have been obtained with the help of the Adam-Bashforth method. Lastly, the model's simulations have been performed considering various fractional derivative values.