Geodesic
From Differences to Derivatives
Fractional calculus and applied analysis, Tome 7 (2004) no. 4, pp. 459-471.

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

A relation showing that the Grünwald-Letnikov and generalized Cauchy derivatives are equal is deduced confirming the validity of a well known conjecture. Integral representations for both direct and reverse fractional differences are presented. From these the fractional derivative is readily obtained generalizing the Cauchy integral formula.
Keywords: Fractional Difference, Grünwald-Letnikov Derivative, Generalized Cauchy Derivative 
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     author = {Duarte Ortigueira, Manuel and Coito, Fernando},
     title = {From {Differences} to {Derivatives}},
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     language = {en},
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Duarte Ortigueira, Manuel; Coito, Fernando. From Differences to Derivatives. Fractional calculus and applied analysis, Tome 7 (2004) no. 4, pp. 459-471. http://geodesic.mathdoc.fr/item/FCAA_2004_7_4_a5/