publication . Article . 2021

Local existence and uniqueness for a fractional SIRS model with Mittag–Leffler law

Moulay Rchid Sidi Ammi; Mostafa Tahiri; Delfim F. M. Torres;
Open Access English
  • Published: 01 Jun 2021 Journal: General Letters in Mathematics, volume 10, issue 2, pages 61-71 (issn: 2519-9269, eissn: 2519-9277, Copyright policy)
  • Publisher: Refaad
In this paper, we study an epidemic model with Atangana-Baleanu-Caputo fractional derivative. We obtain a special solution using an iterative scheme via Laplace transformation. Uniqueness and existence of a solution using the Banach fixed point theorem are studied. A detailed analysis of the stability of the special solution is presented. Finally, our generalized model in the derivative sense is solved numerically by the Adams-Bashforth-Moulton method.
free text keywords: epidemic model, atangana-baleanu-caputo fractional derivative, fixed point theorem, numerical simulations, Mathematics, QA1-939
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