Analysis of HIV/AIDS model with Mittag-Leffler kernel

Muhammad Mannan Akram; Muhammad Farman; Ali Akgül; Muhammad Umer Saleem; Aqeel Ahmad; Mohammad Partohaghigh; Fahd Jarad; Muhammad Mannan Akram; Muhammad Farman; Ali Akgül; Muhammad Umer Saleem; Aqeel Ahmad; Mohammad Partohaghigh; Fahd Jarad

doi:10.3934/math.2022739

AIMS Mathematics

2022, Volume 7, Issue 7: 13383-13401. doi: 10.3934/math.2022739

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Research article

Analysis of HIV/AIDS model with Mittag-Leffler kernel

1.
Department of Mathematics and statistics, University of Lahore, Lahore-54590, Pakistan
2.
Department of Mathematics, Khawaja Fareed University of Engineering and Information Technology, Rahim Yar Khan, Pakistan
3.
Art and Science Faculty, Department of Mathematics, Siirt University, 56100 Siirt Turkey
4.
Department of Mathematics, University of Education, Lahore, Pakistan
5.
Department of Mathematics, Ghazi University, D.G. Khan, Pakistan
6.
Department of Mathematics, Clarkson University, USA
7.
Department of Mathematics, Çankaya University, 06790 Etimesgut, Ankara, Turkey
8.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

Received: 20 March 2022 Revised: 20 April 2022 Accepted: 04 May 2022 Published: 17 May 2022
MSC : 37C75, 93B05, 65L07

Recently different definitions of fractional derivatives are proposed for the development of real-world systems and mathematical models. In this paper, our main concern is to develop and analyze the effective numerical method for fractional order HIV/ AIDS model which is advanced approach for such biological models. With the help of an effective techniques and Sumudu transform, some new results are developed. Fractional order HIV/AIDS model is analyzed. Analysis for proposed model is new which will be helpful to understand the outbreak of HIV/AIDS in a community and will be helpful for future analysis to overcome the effect of HIV/AIDS. Novel numerical procedures are used for graphical results and their discussion.
- Sumudu transform,
- uniqueness,
- stability analysis,
- fixed-point theorem
Citation: Muhammad Mannan Akram, Muhammad Farman, Ali Akgül, Muhammad Umer Saleem, Aqeel Ahmad, Mohammad Partohaghigh, Fahd Jarad. Analysis of HIV/AIDS model with Mittag-Leffler kernel[J]. AIMS Mathematics, 2022, 7(7): 13383-13401. doi: 10.3934/math.2022739

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Abstract

Recently different definitions of fractional derivatives are proposed for the development of real-world systems and mathematical models. In this paper, our main concern is to develop and analyze the effective numerical method for fractional order HIV/ AIDS model which is advanced approach for such biological models. With the help of an effective techniques and Sumudu transform, some new results are developed. Fractional order HIV/AIDS model is analyzed. Analysis for proposed model is new which will be helpful to understand the outbreak of HIV/AIDS in a community and will be helpful for future analysis to overcome the effect of HIV/AIDS. Novel numerical procedures are used for graphical results and their discussion.

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