Relations between fractional models with three-parameter Mittag-Leffler kernels

Abstract

Abstract We consider two models of fractional calculus which are defined using three-parameter Mittag-Leffler functions: the Prabhakar definition and a recently defined extension of the Atangana–Baleanu definition. By examining the relationships between the two, we are able to find some new properties of both, as well as of the original Atangana–Baleanu model and its iterated form.

Keywords

• Fractional calculus
• Mittag-Leffler functions
• Atangana–Baleanu fractional calculus
• Prabhakar fractional calculus