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A Local Fractional Taylor Expansion and Its Computation for Insufficiently Smooth Functions

Published online by Cambridge University Press:  28 May 2015

Zhifang Liu ,
Tongke Wang  and
Guanghua Gao
Zhifang Liu
Affiliation:
School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, China
Tongke Wang*
Affiliation:
School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, China
Guanghua Gao
Affiliation:
College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
*
*Corresponding author. Email addresses: liuzhifang0628@gmail.com (Z. Liu), wangtke@sina.com (T. Wang), gaoguanghua1107@163.com (G. Gao)
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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

26A3365B05Local fractional derivativecritical orderlocal fractional Taylor expansionAitken delta square methodepsilon algorithm

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Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 5 , Issue 2 , May 2015 , pp. 176 - 191
Copyright
Copyright © Global-Science Press 2015 

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