SOME APPLICATIONS OF GENERALIZED FRACTIONAL CALCULUS OPERATORS TO A NOVEL CLASS OF ANALYTIC FUNCTIONS WITH NEGATIVE COEFFICIENTS

Abstract

In the present paper, by making use of certain operators of generalized fractional calculus, we introduce a novel class ${\cal T}_{\lambda}^{\mu , \varphi , \eta} (n; \alpha )$ of functions which are analytic and univalent in the open unit disk ${\cal U}.$ A necessary and sufficient condition for a function to be in the class ${\cal T}_{\lambda}^{\mu , \varphi , \eta}(n; \alpha )$ is obtained. In addition, this paper includes distortion theorems involving generalized fractional integrals (and generalized fractional derivatives), radii of close-to-convexity, starlikeness, and convexity. Relevance with some new (or known) special cases are also pointed out.