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Improving Variational Iteration Method with Auxiliary Parameter for Nonlinear Time-Fractional Partial Differential Equations

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Abstract

In this research, we present a new approach based on variational iteration method for solving nonlinear time-fractional partial differential equations in large domains. The convergence of the method is shown with the aid of Banach fixed point theorem. The maximum error bound is specified. The optimal value of auxiliary parameter is obtained by use of residual error function. The fractional derivatives are taken in the Caputo sense. Numerical examples that involve the time-fractional Burgers equation, the time-fractional fifth-order Korteweg–de Vries equation and the time-fractional Fornberg–Whitham equation are examined to show the appropriate properties of the method. The results reveal that a new approach is very effective and convenient.

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Authors and Affiliations

  1. Yuzuncu Yıl University, Van, Turkey

    Mehmet Giyas Sakar & Onur Saldır

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  1. Mehmet Giyas Sakar
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  2. Onur Saldır
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Correspondence to Mehmet Giyas Sakar.

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Sakar, M.G., Saldır, O. Improving Variational Iteration Method with Auxiliary Parameter for Nonlinear Time-Fractional Partial Differential Equations. J Optim Theory Appl 174, 530–549 (2017). https://doi.org/10.1007/s10957-017-1127-y

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