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.

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

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