Study of mathematical model of Hepatitis <i>B</i> under Caputo-Fabrizo derivative

Sajjad Ali Khan; Kamal Shah; Poom Kumam; Aly Seadawy; Gul Zaman; Zahir Shah; Sajjad Ali Khan; Kamal Shah; Poom Kumam; Aly Seadawy; Gul Zaman; Zahir Shah

doi:10.3934/math.2021013

AIMS Mathematics

2021, Volume 6, Issue 1: 195-209. doi: 10.3934/math.2021013

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Research article

Study of mathematical model of Hepatitis B under Caputo-Fabrizo derivative

1.
Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtankhawa, Pakistan
2.
KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut's University of Technology, Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
3.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
4.
Department of Mathematics and Statistics, Taibah University, Medina, Saudi Arabia
5.
Department of Mathematics, University of Lakki Marwat, Lakki Marwat 28420, Khyber Pakhtunkhwa, Pakistan

Received: 05 July 2020 Accepted: 14 September 2020 Published: 09 October 2020
MSC : 26A33, 34A08, 93A30

The current work is devoted to bring out a detail analysis including qualitative and semi-analytical study of Hepatitis B model under the Caputo- Fabrizio fractional derivative (CFFD). For the required results, fixed point theory is used to establish the conditions for existence and uniqueness of solution to the considered model. On the other hand, for semi analytical solutions, we use decomposition method of Adomian coupled with integral transform of Laplace. Moreover, the concerned solutions are presented via graphs to analyze the dynamics of different compartments of the model.
- Hepatitis B,
- CFFD,
- existence,
- fixed point theory,
- semi analytical results
Citation: Sajjad Ali Khan, Kamal Shah, Poom Kumam, Aly Seadawy, Gul Zaman, Zahir Shah. Study of mathematical model of Hepatitis B under Caputo-Fabrizo derivative[J]. AIMS Mathematics, 2021, 6(1): 195-209. doi: 10.3934/math.2021013

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Abstract

The current work is devoted to bring out a detail analysis including qualitative and semi-analytical study of Hepatitis B model under the Caputo- Fabrizio fractional derivative (CFFD). For the required results, fixed point theory is used to establish the conditions for existence and uniqueness of solution to the considered model. On the other hand, for semi analytical solutions, we use decomposition method of Adomian coupled with integral transform of Laplace. Moreover, the concerned solutions are presented via graphs to analyze the dynamics of different compartments of the model.

References

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