A fractional model for the dynamics of COVID-19 using Atangana-Baleanu fractional operators

Volume 39, Issue 2, pp 233--248 https://dx.doi.org/10.22436/jmcs.039.02.04

Publication Date: March 29, 2025 Submission Date: July 28, 2024 Revision Date: August 24, 2024 Accteptance Date: January 14, 2025

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Authors

Sh. Ahmed - Department of Mathematics, Central University of Haryana, Mahendergarh-123029, India. Sh. Jahan - Department of Mathematics, Central University of Haryana, Mahendergarh-123029, India. K. S. Nisar - Department of Mathematics, College of Sciences and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia. - Hourani Center for Applied Scientific Research, Al-Ahliyya Amman University, Jordan.

Abstract

This paper analyzes models that address key challenges in global healthcare related to COVID-19 and offers insights for developing effective response strategies. Our primary objective is to apply the Atangana-Baleanu-Caputo (ABC) fractional derivative, incorporating the Mittag-Leffler kernel, to conduct an in-depth analysis of the COVID-19 model. The Picard-Lindelof approach is used to do a comprehensive study of the existence and uniqueness of the model's solutions. The ABC operator, combining the fundamental theorem of fractional calculus with two-step Lagrange polynomial interpolation, was applied to estimate the solutions of the nonlinear fractional-order COVID-19 model. The behavior of the model is depicted through figures. The findings demonstrate that this method is both powerful and straightforward when applied to nonlinear equations. Furthermore, the results confirm the viability of the ABC fractional operator for mathematical epidemiology and its potential use in other real-world problems.

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Keywords

• Atangana-Baleanu fractional operators
• COVID-19 disease
• fractional calculus
• numerical simulation
• Mittag-Leffler kernel
• mathematical epidemiology

MSC

•  26A33
•  34C60
•  92C60
•  92D30

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