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      On modeling of coronavirus-19 disease under Mittag-Leffler power law

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          Abstract

          This paper investigates a new model on coronavirus-19 disease (COVID-19) with three compartments including susceptible, infected, and recovered class under Mittag-Leffler type derivative. The mentioned derivative has been introduced by Atangana, Baleanu, and Caputo abbreviated as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(\mathcal{ABC})$\end{document} . Upon utilizing fixed point theory, we first prove the existence of at least one solution for the considered model and its uniqueness. Also, some results about stability of Ulam–Hyers type are also established. By applying a numerical technique called fractional Adams–Bashforth (AB) method, we develop a scheme for the approximate solutions to the considered model. Using some real available data, we perform the concerned numerical simulation corresponding to different values of fractional order.

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          Most cited references 29

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          Solution of the epidemic model by Adomian decomposition method

           J. Biazar (2006)
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            Numerical approximation of Riemann-Liouville definition of fractional derivative: From Riemann-Liouville to Atangana-Baleanu: Atangana and Gómez-Aguilar

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              Fractional operators with exponential kernels and a Lyapunov type inequality

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                Author and article information

                Contributors
                s.bushnaq@psut.edu.jo
                kamalshah408@gmail.com
                hussam89@yahoo.com
                Journal
                Adv Differ Equ
                Adv Differ Equ
                Advances in Difference Equations
                Springer International Publishing (Cham )
                1687-1839
                1687-1847
                11 September 2020
                11 September 2020
                2020
                : 2020
                : 1
                Affiliations
                [1 ]GRID grid.29251.3d, ISNI 0000 0004 0404 9637, Department of Basic Sciences, King Abdullah II for Engineering, , Princess Sumaya University for Technology, ; Amman, 11941 Jordan
                [2 ]GRID grid.440567.4, ISNI 0000 0004 0607 0608, Department of Mathematics, , University of Malakand, Dir(L), ; 18000 Khyber Pakhtunkhwa, Pakistan
                [3 ]Al Ain University, Al Ain, UAE
                [4 ]GRID grid.449604.b, ISNI 0000 0004 0421 7127, Mathematics Department, , Tafila Technical University, ; Tafila, Jordan
                Article
                2943
                10.1186/s13662-020-02943-z
                7483517
                © The Author(s) 2020

                Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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                © The Author(s) 2020

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