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

  • Badr Saad T. Alkahtani
Regular Article
Part of the following topical collections:
  1. Focus Point on Modelling Complex Real-World Problems with Fractal and New Trends of Fractional Differentiation

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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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, College of ScienceKing Saud UniversityRiyadhSaudi Arabia

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