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 - <p style="text-align: justify;">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.</p>