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An iterative approximation for time-fractional Cahn–Allen equation with reproducing kernel method

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Abstract

In this article, we construct a novel iterative approach that depends on reproducing kernel method for Cahn–Allen equation with Caputo derivative. Representation of solution and convergence analysis are presented theoretically. Numerical results are given as tables and graphics with intent to show efficiency and power of method. The results demonstrate that approximate solution uniformly converges to exact solution for Cahn–Allen equation with fractional derivative.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Yuzuncu Yil University, Van, 65080, Turkey

    Mehmet Giyas Sakar & Onur Saldır

  2. Department of Statistics, Faculty of Sciences, Yuzuncu Yil University, Van, 65080, Turkey

    Fevzi Erdogan

Authors
  1. Mehmet Giyas Sakar
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  2. Onur Saldır
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  3. Fevzi Erdogan
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Correspondence to Mehmet Giyas Sakar.

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Communicated by José Tenreiro Machado.

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Sakar, M.G., Saldır, O. & Erdogan, F. An iterative approximation for time-fractional Cahn–Allen equation with reproducing kernel method. Comp. Appl. Math. 37, 5951–5964 (2018). https://doi.org/10.1007/s40314-018-0672-9

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  • DOI: https://doi.org/10.1007/s40314-018-0672-9

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