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Comparison of numerical techniques for the solution of a fractional epidemic model

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Abstract

The purpose of the proposed paper is to analyze the dynamics of an epidemic model with fractional and fractal–fractional order by considering two different numerical approaches. Initially, we consider an epidemic model in fractional Atangana–Baleanu derivative and then obtain the necessary results associated with the model. Stability results for the model are obtained and showed that the model is stable when the basic reproduction number is less than unity. Then, we apply the new idea of fractal–fractional to the influenza model in the sense of Atangana–Baleanu fractional operator. The model with fractional and fractal–fractional operators is solved with numerical techniques. We present graphical results for fractional model with many values of \(\theta \). For the fractal–fractional model, we present a different set of fractal and fractional order to obtain graphical results. Further, we provide a comparison among the operators with novel numerical procedure considering different orders of \(\theta \). We conclude that the idea of fractal–fractional provides powerful results than that of fractional and integer-order derivative.

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Acknowledgements

This project was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under Grant No. D-112-130-1440. The authors, therefore, gratefully acknowledge the DSR for technical and financial support.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah, 21589, Saudi Arabia

    Ebraheem O. Alzahrani

  2. Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa

    M. A. Khan

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  1. Ebraheem O. Alzahrani
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  2. M. A. Khan
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Correspondence to M. A. Khan.

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Alzahrani, E.O., Khan, M.A. Comparison of numerical techniques for the solution of a fractional epidemic model. Eur. Phys. J. Plus 135, 110 (2020). https://doi.org/10.1140/epjp/s13360-020-00183-4

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