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An application of variational iteration method for solving fuzzy time-fractional diffusion equations

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Abstract

In this paper, an approximate solution based on the variational iteration method is given to solve the fuzzy time-fractional diffusion equations. The time-fractional derivative is taken in the Caputo sense. In the variational iteration method, the solution appears as a convergent series with easily predictable terms. In this approach, the correctional functional is constructed and the Lagrange multiplier is identified optimally via variational theory. Some examples are also given to illustrate the performance and applicability of the proposed method for the discussed class of fuzzy time-fractional diffusion equations. To demonstrate the efficiency of the variational iteration method, comparisons have been made with the numerical solution obtained by the implicit finite difference scheme that exists in the literature. The proposed iterative algorithm is quite simple to use and does not require any discretization, transformation, or restrictive assumptions. Also, tabulated results show that the proposed algorithm gives better accuracy than the implicit finite difference scheme.

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Acknowledgements

The authors are thankful to the anonymous referees for their valuable suggestions to improve the paper.

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  1. Center for Mathematical and Financial Computing, Department of Mathematics, The LNM Institute of Information Technology, Jaipur, 302031, India

    Saurabh Kumar & Vikas Gupta

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  1. Saurabh Kumar
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  2. Vikas Gupta
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Correspondence to Vikas Gupta.

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Kumar, S., Gupta, V. An application of variational iteration method for solving fuzzy time-fractional diffusion equations. Neural Comput & Applic 33, 17659–17668 (2021). https://doi.org/10.1007/s00521-021-06354-3

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