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Generalizing Grünwald-Letnikov's formulas for fractional derivatives

Marie Christine Neel, Maminirina Joelson
Grünwald-Letnikov's formulas yield approximations to Marchaud's derivatives, in the form of discrete convolutions of mesh l, divided by some power of l. A continuous variant of that formulas is presented, with integrals instead of series. It involves convolution kernels which mimic essential properties of Grünwald-Letnikov's weights, but are more general.
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