Fractional Calculus of Analytic Functions Concerned with Möbius Transformations

Abstract

Let A be the class of functions f(z) in the open unit disk U with f(0)=0 and f′(0)=1. Also, let w(ζ) be a Möbius transformation in U for some z∈U. Applying the Möbius transformations, we consider some properties of fractional calculus (fractional derivatives and fractional integrals) of f(z)∈A. Also, some interesting examples for fractional calculus are given.