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Numerical approximation to the fractional derivative operator

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Abstract

In this paper we consider the numerical approximation of \(A^{\alpha }\) by contour integral. We are mainly interested to the case of \(A\) representing the discretization of the first derivative by means of a backward differentiation formula, and \( 0\!<\!\alpha \!<\!1\). The computation of the contour integral yields a rational approximation to \(A^{\alpha }\) which can be used to define \(k\)-step formulas for the numerical integration of Fractional Differential Equations.

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Acknowledgments

The author is grateful to Igor Moret for some helpful discussions.

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  1. Department of Mathematics, University of Padova, Padua, Italy

    P. Novati

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  1. P. Novati
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Novati, P. Numerical approximation to the fractional derivative operator. Numer. Math. 127, 539–566 (2014). https://doi.org/10.1007/s00211-013-0596-7

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