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

Abstract : 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.
Document type :
Journal articles
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https://hal.inria.fr/hal-00724710
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Submitted on : Wednesday, August 22, 2012 - 1:54:52 PM
Last modification on : Thursday, May 2, 2019 - 2:14:36 PM

### Citation

Shakoor Pooseh, Ricardo Almeida, Delfim F. M. Torres. Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative. Numerical Functional Analysis and Optimization, Taylor & Francis, 2012, 33 (3), pp.301-319. ⟨10.1080/01630563.2011.647197⟩. ⟨hal-00724710⟩

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