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Expansion formulas in terms of integer-order derivatives for the Hadamard fractional integral and derivative. (English) Zbl 1248.26013

The authors obtain series expansion formulas for the Hadamard fractional integral and fractional derivative of smooth functions. Their approach is to seek expansion formulae for the Hadamard fractional operators with integer order derivatives. Decomposition formulae for the left and right Hadamard fractional integrals are given, with approximation formulae and error estimations. Some examples are given to show the efficiency of such approximations.

MSC:

26A33 Fractional derivatives and integrals
33F05 Numerical approximation and evaluation of special functions
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References:

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