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Atangana-Batogna numerical scheme applied on a linear and non-linear fractional differential equation

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Abstract.

Recently, Atangana and Batogna suggested a new numerical scheme to solve linear and non-linear equations with classical and fractional differential operators. The method can be understood as a combination of forward (or backward) approximation and the Adams-Bashforth one. This paper further presents the application of the new method to a linear and non-linear partial differential equation with integer- and non-integer-order derivative. The stability and convergence analyses are presented in detail. Some simulations are done to verify the efficiency of the new numerical scheme for solving linear and non-linear equations.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, King Saud University, P.O.Box 1142, 11989, Riyadh, Saudi Arabia

    Badr Saad T. Alkahtani

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  1. Badr Saad T. Alkahtani
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Correspondence to Badr Saad T. Alkahtani.

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Alkahtani, B.S.T. Atangana-Batogna numerical scheme applied on a linear and non-linear fractional differential equation. Eur. Phys. J. Plus 133, 111 (2018). https://doi.org/10.1140/epjp/i2018-11961-8

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  • DOI: https://doi.org/10.1140/epjp/i2018-11961-8

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