An Extension to the Owa-Srivastava Fractional Operator with Applications to Parabolic Starlike and Uniformly Convex Functions

Abstract EN

Let ? be the class of analytic functions in the open unit disk ?.

We define Θα,β:?→? by (Θα,βf)(z):=Γ(2−α)zαDzα(Γ(2−β)zβDzβf(z)),(α,β≠2,3,4…), where Dzγf is the fractional derivative of f of order γ.

If α,β∈[0,1], then a function f in ? is said to be in the class SPα,β if Θα,βf is a parabolic starlike function.

In this paper, several properties and characteristics of the class SPα,β are investigated.

These include subordination, characterization and inclusions, growth theorems, distortion theorems, and class-preserving operators.

Furthermore, sandwich theorem related to the fractional derivative is proved.