GENERALIZING GR ¨ UNWALD-LETNIKOV'S FORMULAS FOR FRACTIONAL DERIVATIVES

Grunwald-Letnikov's formulas yield approximations to Marchaud's derivatives, in the form of discrete con- volutions of mesh l, multiplied by l −α . A continu- ous variant of that formulas is presented, with inte- grals instead of series. It involves convolution ker- nels which mimic essential properties of Grunwald- Letnikov's weights, but are more general.