Applications of fractional calculus to $ k $-uniformly starlike and $ k $-uniformly convex functions of order $ \alpha $

Abstract

A new subclass of analytic functions $ k-SP_\lambda(\alpha) $ is introduced by applying certain operators of fractional calculus to $k$-uniformly starlike and $ k $-uniformly convex functions of order $ \alpha $. Some theorems on coefficient bounds and growth and distortion theorems for this subclass are found. The radii of close to convexity, starlikeness and convexity for this subclass is also derived.