Differintegration with Respect to Functions in Fractional Models Involving Mittag-Leffler Functions

Abstract

We consider what it means to fractionally differentiate or integrate one function with respect to another function, in models of fractional calculus which involve Mittag-Leffler kernels. Using our presented definitions, we derive series expressions for such differ-integrals, which we then use to prove some important results such as an elegant formulation of the fractional chain rule.