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On fractional Wirtinger derivatives for complex analysis

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FDE2 - Fractional differential equations

Despite its importance in mathematics, complex analysis is a field which has not been much explored from the fractional viewpoint. Complex-order fractional differintegrals are well known; fractional differintegrals of complex functions are also fairly standard; but many of the specialised facts and operations of complex analysis have had no fractional analogues. We consider the Wirtinger derivatives (in particular, the complex d-bar derivative) and how to define fractional versions of these operators. To motivate and justify the definitions, we compare their properties both with the original d-bar and Wirtinger derivatives and with the original fractional calculus, noting that the natural analogues emerge as expected. Potential applications will also be discussed. Joint work with Chaima Bouzouina.

This talk is part of the Isaac Newton Institute Seminar Series series.

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