Epidemiological analysis of fractional order COVID-19 model with Mittag-Leffler kernel

Muhammad Farman; Ali Akgül; Kottakkaran Sooppy Nisar; Dilshad Ahmad; Aqeel Ahmad; Sarfaraz Kamangar; C Ahamed Saleel; Muhammad Farman; Ali Akgül; Kottakkaran Sooppy Nisar; Dilshad Ahmad; Aqeel Ahmad; Sarfaraz Kamangar; C Ahamed Saleel

doi:10.3934/math.2022046

AIMS Mathematics

2022, Volume 7, Issue 1: 756-783. doi: 10.3934/math.2022046

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Research article

Epidemiological analysis of fractional order COVID-19 model with Mittag-Leffler kernel

1.
Department of Mathematics and Statistics, University of Lahore, Lahore-54590, Pakistan
2.
Art and Science Faculty, Department of Mathematics, Siirt University, 56100 Siirt Turkey
3.
Department of Mathematics, College of Arts and Sciences, Wadi Aldawaser, 11991, Prince Sattam bin Abdulaziz University, Saudi Arabia
4.
Department of Mechanical Engineering, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia

Received: 08 August 2021 Accepted: 30 September 2021 Published: 15 October 2021
MSC : 37C75, 93B05, 93B07, 65L07

This paper derived fractional derivatives with Atangana-Baleanu, Atangana-Toufik scheme and fractal fractional Atangana-Baleanu sense for the COVID-19 model. These are advanced techniques that provide effective results to analyze the COVID-19 outbreak. Fixed point theory is used to derive the existence and uniqueness of the fractional-order model COVID-19 model. We also proved the property of boundedness and positivity for the fractional-order model. The Atangana-Baleanu technique and Fractal fractional operator are used with the Sumudu transform to find reliable results for fractional order COVID-19 Model. The generalized Mittag-Leffler law is also used to construct the solution with the different fractional operators. Numerical simulations are performed for the developed scheme in the range of fractional order values to explain the effects of COVID-19 at different fractional values and justify the theoretical outcomes, which will be helpful to understand the outbreak of COVID-19 and for control strategies.
- COVID-19,
- Sumudu transform,
- ABC derivative,
- fractal operator,
- stability and uniqueness,
- Mittag-Leffler law
Citation: Muhammad Farman, Ali Akgül, Kottakkaran Sooppy Nisar, Dilshad Ahmad, Aqeel Ahmad, Sarfaraz Kamangar, C Ahamed Saleel. Epidemiological analysis of fractional order COVID-19 model with Mittag-Leffler kernel[J]. AIMS Mathematics, 2022, 7(1): 756-783. doi: 10.3934/math.2022046

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Abstract

This paper derived fractional derivatives with Atangana-Baleanu, Atangana-Toufik scheme and fractal fractional Atangana-Baleanu sense for the COVID-19 model. These are advanced techniques that provide effective results to analyze the COVID-19 outbreak. Fixed point theory is used to derive the existence and uniqueness of the fractional-order model COVID-19 model. We also proved the property of boundedness and positivity for the fractional-order model. The Atangana-Baleanu technique and Fractal fractional operator are used with the Sumudu transform to find reliable results for fractional order COVID-19 Model. The generalized Mittag-Leffler law is also used to construct the solution with the different fractional operators. Numerical simulations are performed for the developed scheme in the range of fractional order values to explain the effects of COVID-19 at different fractional values and justify the theoretical outcomes, which will be helpful to understand the outbreak of COVID-19 and for control strategies.

References

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