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Modeling and analysis of the fractional HBV model with Atangana-Baleanu derivative

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Abstract.

Recently a new fractional derivative with non-local and non-singular kernel was proposed by Atangana and Baleanu. In this paper, a fractional hepatitis B virus model with Atangana-Baleanu derivative (AB derivative) is formulated. Initially, we present the model equilibria and basic reproduction number. The local stability of the disease-free equilibrium point is proved using Matignon’s conditions. The fixed-point theory is applied to show the existence and uniqueness of solutions for the fractional HBV disease model. A numerical scheme using Adams-Bashforth method for solving the proposed fractional model involving the AB derivative is presented. Finally, numerical simulations are performed in order to validate the importance of the arbitrary order derivative. The fractional-order derivative provides more information about the complexity of the dynamics of the proposed HBV model.

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Authors and Affiliations

  1. Department of Mathematics, University of Peshawar, Peshawar, KP, Pakistan

    Saif Ullah & Muhammad Farooq

  2. Department of Mathematics, City University of Science and Information Technology, Peshawar, KP, Pakistan

    Muhammad Altaf Khan

Authors
  1. Saif Ullah
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  2. Muhammad Altaf Khan
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  3. Muhammad Farooq
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Correspondence to Muhammad Altaf Khan.

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Ullah, S., Altaf Khan, M. & Farooq, M. Modeling and analysis of the fractional HBV model with Atangana-Baleanu derivative. Eur. Phys. J. Plus 133, 313 (2018). https://doi.org/10.1140/epjp/i2018-12120-1

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  • DOI: https://doi.org/10.1140/epjp/i2018-12120-1

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