Riesz Potentials as Centred Derivatives
- Citation:
- Ortigueira, MD. 2007. Riesz Potentials as Centred Derivatives. Advances in Fractional Calculus. :93–112.: Springer Netherlands
Abstract:
Generalised fractional centred differences and derivatives are studied in this Chapter. These generalise to real orders the existing ones valid for even and odd positive integer orders. For each one, suitable integral formulations are presented. The limit computation inside the integrals leads to generalisations of the Cauchy derivative. Their computations using a special path lead to the well known Riesz potentials. A study for coherence is done by applying the definitions to functions with Fourier transform. The existence of inverse Riesz potentials is also studied.
Notes:
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