A complex analysis approach to Atangana-Baleanu fractional calculus

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.

18 pages. Accepted for publication in Mathematical Methods in the Applied Sciences

References in corpus (3)

• On some new properties of fractional derivatives with Mittag-Leffler kernel
• On fractional calculus with general analytic kernels
• The role of fractional time-derivative operators on anomalous diffusion