Fractional Calculus of Analytic Functions Concerned with Möbius Transformations

Abstract EN

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.