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arXiv · 1905.06834

A complex analysis approach to Atangana-Baleanu fractional calculus

Arran Fernandez
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Abstract

The standard definition for the Atangana-Baleanu fractional derivative involves an integral transform with a Mittag-Leffler function in the kernel. We show that this integral can be rewritten as a complex contour integral which can be used to provide an analytic continuation of the definition to complex orders of differentiation. We discuss the implications and consequences of this extension, including a more natural formula for the Atangana-Baleanu fractional integral and for iterated Atangana-Baleanu fractional differintegrals.

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Arran Fernandez. 2019-05-16. A complex analysis approach to Atangana-Baleanu fractional calculus. https://doi.org/10.1002/mma.5754

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