Stability analysis of COVID-19 outbreak using Caputo-Fabrizio fractional differential equation

Murugesan Sivashankar; Sriramulu Sabarinathan; Vediyappan Govindan; Unai Fernandez-Gamiz; Samad Noeiaghdam; Murugesan Sivashankar; Sriramulu Sabarinathan; Vediyappan Govindan; Unai Fernandez-Gamiz; Samad Noeiaghdam

doi:10.3934/math.2023143

AIMS Mathematics

2023, Volume 8, Issue 2: 2720-2735. doi: 10.3934/math.2023143

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Stability analysis of COVID-19 outbreak using Caputo-Fabrizio fractional differential equation

1.
Department of Mathematics, SRM Institute of Science & Technology, Kattankulthur-603 203, Tamil Nadu, India
2.
Department of Mathematics, DMI St John The Baptist University Central Mangochi-409, Central Africa, Malawi
3.
Nuclear Engineering and Fluid Mechanics Department, University of the Basque Country UPV/EHU, Nieves Cano 12, 01006 Vitoria-Gasteiz, Spain
4.
Department of Applied Mathematics and Programming, South Ural State University, Lenin prospect 76, Chelyabinsk, 454080, Russia

Received: 31 July 2022 Revised: 17 September 2022 Accepted: 08 October 2022 Published: 09 November 2022
MSC : 26A33, 34A08, 65L07, 92D25, 34K20

The main aim of this paper is to construct a mathematical model for the spread of SARS-CoV-2 infection. We discuss the modified COVID-19 and change the model to fractional order form based on the Caputo-Fabrizio derivative. Also several definitions and theorems of fractional calculus, fuzzy theory and Laplace transform are illustrated. The existence and uniqueness of the solution of the model are proved based on the Banach's unique fixed point theory. Moreover Hyers-Ulam stability analysis is studied. The obtained results show the efficiency and accuracy of the model.
- Hyers-Ulam stability,
- variable Caputo-Fabrizio fractional derivative,
- Banach fixed point theorem,
- unit step function,
- existence and uniqueness
Citation: Murugesan Sivashankar, Sriramulu Sabarinathan, Vediyappan Govindan, Unai Fernandez-Gamiz, Samad Noeiaghdam. Stability analysis of COVID-19 outbreak using Caputo-Fabrizio fractional differential equation[J]. AIMS Mathematics, 2023, 8(2): 2720-2735. doi: 10.3934/math.2023143

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Abstract

The main aim of this paper is to construct a mathematical model for the spread of SARS-CoV-2 infection. We discuss the modified COVID-19 and change the model to fractional order form based on the Caputo-Fabrizio derivative. Also several definitions and theorems of fractional calculus, fuzzy theory and Laplace transform are illustrated. The existence and uniqueness of the solution of the model are proved based on the Banach's unique fixed point theory. Moreover Hyers-Ulam stability analysis is studied. The obtained results show the efficiency and accuracy of the model.

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