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New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models

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Abstract.

Recently a new concept of fractional differentiation with non-local and non-singular kernel was introduced in order to extend the limitations of the conventional Riemann-Liouville and Caputo fractional derivatives. A new numerical scheme has been developed, in this paper, for the newly established fractional differentiation. We present in general the error analysis. The new numerical scheme was applied to solve linear and non-linear fractional differential equations. We do not need a predictor-corrector to have an efficient algorithm, in this method. The comparison of approximate and exact solutions leaves no doubt believing that, the new numerical scheme is very efficient and converges toward exact solution very rapidly.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Science, Université Moulay Ismail, B.P. 11201, Zitoune Meknès, Morocco

    Mekkaoui Toufik

  2. Institute for groundwater studied, Faculty of Natural and Agricultural Science, University of Free State, 9300, Bloemfontein, South Africa

    Abdon Atangana

Authors
  1. Mekkaoui Toufik
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  2. Abdon Atangana
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Correspondence to Abdon Atangana.

Additional information

The original online version of this article was revised to correct equation 14.

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Toufik, M., Atangana, A. New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models. Eur. Phys. J. Plus 132, 444 (2017). https://doi.org/10.1140/epjp/i2017-11717-0

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