A Novel Subclass of Analytic Functions Specified by a Family of Fractional Derivatives in the Complex Domain

Abstract

In this paper, by making use of a certain family of fractionalderivative operators in the complex domain, we introduce andinvestigate a new subclass $\mathcal{P}_{\tau,\mu}(k,\delta,\gamma)$ of analytic and univalent functions in the open unit disk $\mathbb{U}$. In particular, for functions in the class$\mathcal{P}_{\tau,\mu}(k,\delta,\gamma)$, we derive sufficient coefficient inequalities and coefficient estimates, distortion theorems involving theabove-mentioned fractional derivative operators, and the radiiof starlikeness and convexity. In addition, some applications offunctions in the class $\mathcal{P}_{\tau,\mu}(k,\delta,\gamma)$ are also pointed out.