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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