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Two New Approximations for Variable-Order Fractional Derivatives

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  • Ruilian Du
  • Zongqi Liang

Abstract

We introduced a parameter which was related to ; then two numerical schemes for variable-order Caputo fractional derivatives were derived; the second-order numerical approximation to variable-order fractional derivatives and -order approximation for are established. For the given parameter , the error estimations of formulas were proven, which were higher than some recently derived schemes. Finally, some numerical examples with exact solutions were studied to demonstrate the theoretical analysis and verify the efficiency of the proposed methods.

Suggested Citation

  • Ruilian Du & Zongqi Liang, 2017. "Two New Approximations for Variable-Order Fractional Derivatives," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-10, July.
    • Handle: RePEc:hin:jnddns:1586249
    DOI: 10.1155/2017/1586249
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    References listed on IDEAS

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    1. Sun, HongGuang & Chen, Wen & Chen, YangQuan, 2009. "Variable-order fractional differential operators in anomalous diffusion modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4586-4592.
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