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Volume 5, Issue 2
A Local Fractional Taylor Expansion and Its Computation for Insufficiently Smooth Functions

Zhifang Liu, Tongke Wang & Guanghua Gao

DOI: 10.4208/eajam.060914.260415a

East Asian J. Appl. Math., 5 (2015), pp. 176-191.

Published online: 2018-02

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  • Abstract

A general fractional Taylor formula and its computation for insufficiently smooth functions are discussed. The Aitken delta square method and epsilon algorithm are implemented to compute the critical orders of the local fractional derivatives, from which more critical orders are recovered by analysing the regular pattern of the fractional Taylor formula. The Richardson extrapolation method is used to calculate the local fractional derivatives with critical orders. Numerical examples are provided to verify the theoretical analysis and the effectiveness of our approach.

  • Keywords

Local fractional derivative, critical order, local fractional Taylor expansion, Aitken delta square method, epsilon algorithm.

  • AMS Subject Headings

26A33, 65B05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-5-176, author = {Zhifang Liu, Tongke Wang and Guanghua Gao}, title = {A Local Fractional Taylor Expansion and Its Computation for Insufficiently Smooth Functions}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {5}, number = {2}, pages = {176--191}, abstract = {

A general fractional Taylor formula and its computation for insufficiently smooth functions are discussed. The Aitken delta square method and epsilon algorithm are implemented to compute the critical orders of the local fractional derivatives, from which more critical orders are recovered by analysing the regular pattern of the fractional Taylor formula. The Richardson extrapolation method is used to calculate the local fractional derivatives with critical orders. Numerical examples are provided to verify the theoretical analysis and the effectiveness of our approach.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.060914.260415a}, url = {http://global-sci.org/intro/article_detail/eajam/10793.html} }
TY - JOUR T1 - A Local Fractional Taylor Expansion and Its Computation for Insufficiently Smooth Functions AU - Zhifang Liu, Tongke Wang & Guanghua Gao JO - East Asian Journal on Applied Mathematics VL - 2 SP - 176 EP - 191 PY - 2018 DA - 2018/02 SN - 5 DO - http://doi.org/10.4208/eajam.060914.260415a UR - https://global-sci.org/intro/article_detail/eajam/10793.html KW - Local fractional derivative, critical order, local fractional Taylor expansion, Aitken delta square method, epsilon algorithm. AB -

A general fractional Taylor formula and its computation for insufficiently smooth functions are discussed. The Aitken delta square method and epsilon algorithm are implemented to compute the critical orders of the local fractional derivatives, from which more critical orders are recovered by analysing the regular pattern of the fractional Taylor formula. The Richardson extrapolation method is used to calculate the local fractional derivatives with critical orders. Numerical examples are provided to verify the theoretical analysis and the effectiveness of our approach.

Zhifang Liu, Tongke Wang and Guanghua Gao. (2018). A Local Fractional Taylor Expansion and Its Computation for Insufficiently Smooth Functions. East Asian Journal on Applied Mathematics. 5 (2). 176-191. doi:10.4208/eajam.060914.260415a
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