Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative

Details Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative

2011-12-03

arxiv.org/abs/1112.0693v1

Numer. Funct. Anal. Optim. 33 (2012), no. 3, 301--319

Mathematics

Classical Analysis and ODEs

Submitted 25-Jul-2011; revised 28-Nov-2011; accepted 02-Dec-2011; for publication in Numerical Functional Analysis and Optimiz

Scientific paper

10.1080/01630563.2011.647197

We obtain series expansion formulas for the Hadamard fractional integral and
fractional derivative of a smooth function. When considering finite sums only,
an upper bound for the error is given. Numerical simulations show the
efficiency of the approximation method.

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