Fractal fractional-order derivative for HIV/AIDS model with Mittag-Leffler kernel

Muhammad Farman; Ali Akgül; Merve Taştan Tekin; Muhammad Mannan Akram; Aqeel Ahmad; Emad E. Mahmoud; Ibrahim S. Yahia

doi:10.1016/j.aej.2022.04.030

Fractal fractional-order derivative for HIV/AIDS model with Mittag-Leffler kernel

Muhammad Farman
, Ali Akgül
, Merve Taştan Tekin
, Muhammad Mannan Akram
, Aqeel Ahmad
, Emad E. Mahmoud
, Ibrahim S. Yahia

The University of Lahore
Khwaja Fareed University of Engineering & Information Technology
Siirt University
Ghazi University
Taif University
King Khalid University
Ain Shams University

Research output: Contribution to journal › Article › peer-review

75 Scopus citations

Abstract

In this paper, HIV/AIDS fractional-order model is studied. This epidemic phenomenon is analyzed using Caputo-Fabrizio and Fractal fractional derivative operator that includes an antiretroviral treatment compartment. The advanced approach is used for HIV/AIDS fractional-order model to get reliable outcomes with the help of sumudu transform. The fractional-order HIV/AIDS model is analyzed qualitatively as well as verify unique solutions. Numerical simulations are performed to explain the effects of changing the fractional-order and to support the theoretical results using proposed methods for a range of fractional orders. Also, the comparison has been made with classical order derivative to check the effectiveness of the proposed method for HIV/AIDS.

Original language	English
Pages (from-to)	10965-10980
Number of pages	16
Journal	Alexandria Engineering Journal
Volume	61
Issue number	12
DOIs	https://doi.org/10.1016/j.aej.2022.04.030
State	Published - Dec 2022
Externally published	Yes

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

Fractal fractional
Simulation
Stability
Sumudu transforms
Uniqueness

Access to Document

10.1016/j.aej.2022.04.030

Cite this

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title = "Fractal fractional-order derivative for HIV/AIDS model with Mittag-Leffler kernel",

abstract = "In this paper, HIV/AIDS fractional-order model is studied. This epidemic phenomenon is analyzed using Caputo-Fabrizio and Fractal fractional derivative operator that includes an antiretroviral treatment compartment. The advanced approach is used for HIV/AIDS fractional-order model to get reliable outcomes with the help of sumudu transform. The fractional-order HIV/AIDS model is analyzed qualitatively as well as verify unique solutions. Numerical simulations are performed to explain the effects of changing the fractional-order and to support the theoretical results using proposed methods for a range of fractional orders. Also, the comparison has been made with classical order derivative to check the effectiveness of the proposed method for HIV/AIDS.",

keywords = "Fractal fractional, Simulation, Stability, Sumudu transforms, Uniqueness",

author = "Muhammad Farman and Ali Akg{\"u}l and Tekin, \{Merve Ta{\c s}tan\} and Akram, \{Muhammad Mannan\} and Aqeel Ahmad and Mahmoud, \{Emad E.\} and Yahia, \{Ibrahim S.\}",

note = "Publisher Copyright: {\textcopyright} 2022 THE AUTHORS",

year = "2022",

month = dec,

doi = "10.1016/j.aej.2022.04.030",

language = "English",

volume = "61",

pages = "10965--10980",

journal = "Alexandria Engineering Journal",

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T1 - Fractal fractional-order derivative for HIV/AIDS model with Mittag-Leffler kernel

AU - Farman, Muhammad

AU - Akgül, Ali

AU - Tekin, Merve Taştan

AU - Akram, Muhammad Mannan

AU - Ahmad, Aqeel

AU - Mahmoud, Emad E.

AU - Yahia, Ibrahim S.

PY - 2022/12

Y1 - 2022/12

N2 - In this paper, HIV/AIDS fractional-order model is studied. This epidemic phenomenon is analyzed using Caputo-Fabrizio and Fractal fractional derivative operator that includes an antiretroviral treatment compartment. The advanced approach is used for HIV/AIDS fractional-order model to get reliable outcomes with the help of sumudu transform. The fractional-order HIV/AIDS model is analyzed qualitatively as well as verify unique solutions. Numerical simulations are performed to explain the effects of changing the fractional-order and to support the theoretical results using proposed methods for a range of fractional orders. Also, the comparison has been made with classical order derivative to check the effectiveness of the proposed method for HIV/AIDS.

AB - In this paper, HIV/AIDS fractional-order model is studied. This epidemic phenomenon is analyzed using Caputo-Fabrizio and Fractal fractional derivative operator that includes an antiretroviral treatment compartment. The advanced approach is used for HIV/AIDS fractional-order model to get reliable outcomes with the help of sumudu transform. The fractional-order HIV/AIDS model is analyzed qualitatively as well as verify unique solutions. Numerical simulations are performed to explain the effects of changing the fractional-order and to support the theoretical results using proposed methods for a range of fractional orders. Also, the comparison has been made with classical order derivative to check the effectiveness of the proposed method for HIV/AIDS.

KW - Fractal fractional

KW - Simulation

KW - Stability

KW - Sumudu transforms

KW - Uniqueness

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DO - 10.1016/j.aej.2022.04.030

M3 - Article

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VL - 61

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EP - 10980

JO - Alexandria Engineering Journal

JF - Alexandria Engineering Journal

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ER -

Fractal fractional-order derivative for HIV/AIDS model with Mittag-Leffler kernel

Abstract

UN SDGs

Keywords

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