Abstract
Fractional centred differences and derivatives definitions are proposed, generalizing to real orders the existing ones valid for even and odd positive integer orders. For each one, suitable integral formulations are obtained. The computations of the involved integrals lead to new generalizations of the Cauchy integral derivative. To compute this integral, a special two-straight-line path was used. With this the referred integrals lead to the well-known Riesz potential operators and their inverses that emerge as true fractional centred derivatives, but that can be computed through summations similar to the well-known Grünwald-Letnikov derivatives.
Subject
Mathematics (miscellaneous)
Reference8 articles.
1. Encyclopedia of Mathematics and Its Applications,1999
2. Pure and Applied Mathematics,1974
3. Fourier transforms and the operator Hα
Cited by
217 articles.
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