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Numerical Identification of the Fractional Derivatives in the Two-Dimensional Fractional Cable Equation

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Abstract

In this paper, the two-dimensional fractional cable equation is considered, an efficient numerical method to obtain the identification of the fractional derivatives is investigated. Concerning the numerical treatment of the two-dimensional fractional cable equation, a fourth-order compact finite difference method is proposed, the stability and convergence of the compact difference method are discussed rigorously by means of the Fourier method. For the inverse problem of the identification of the fractional derivatives, Levenberg–Marquardt iterative method is employed, and the fractional sensitivity equation is obtained by means of the digamma function. Finally, numerical examples are presented to show the effectiveness of the proposed numerical method.

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Acknowledgments

The authors wish to express their thanks to the Editor and the anonymous referees for their fruitful advice and comments. The authors express their sincere thanks to Professor Mingrong Cui for his discussion. The project was supported by the National Natural Science Foundation of China (11472161, 11102102 and 91130017) and the Natural Science Foundation of Shandong Province (ZR2015AM011).

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  1. School of Mathematics, Shandong University, Jinan, 250100, China

    Bo Yu & Xiaoyun Jiang

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  1. Bo Yu
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  2. Xiaoyun Jiang
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Correspondence to Xiaoyun Jiang.

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Yu, B., Jiang, X. Numerical Identification of the Fractional Derivatives in the Two-Dimensional Fractional Cable Equation. J Sci Comput 68, 252–272 (2016). https://doi.org/10.1007/s10915-015-0136-y

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  • DOI: https://doi.org/10.1007/s10915-015-0136-y

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