SPECIAL ISSUE PAPER
A complex analysis approach to Atangana–Baleanu fractional calculus
Arran Fernandez,
Corresponding Author
Arran Fernandez
Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, Gazimagusa, TRNC, via Mersin 10 Turkey
Correspondence
Arran Fernandez, Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, Gazimagusa, TRNC, Mersin 10, Turkey.
Email: [email protected] Communicated by: D. Zeidan
Search for more papers by this authorArran Fernandez,
Corresponding Author
Arran Fernandez
Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, Gazimagusa, TRNC, via Mersin 10 Turkey
Correspondence
Arran Fernandez, Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, Gazimagusa, TRNC, Mersin 10, Turkey.
Email: [email protected] Communicated by: D. Zeidan
Search for more papers by this authorAbstract
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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