Some applications of fractional calculus for analytic function

Abstract

For analytic functions f (z) in the class An, fractional calculus (fractional integrals and fractional derivatives) D λ z f (z) of order λ are introduced. Applying D λ z f (z) for f (z) ∈ An, we introduce the interesting subclass An (αm, β, ρ, λ) of An. The object of this paper is to discuss some properties of f (z) concerning D λ z f (z).