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

In this paper, by making use of a certain family of fractional derivative operators in the complex domain, we introduce and investigate 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, distortion theorems involving the above-mentioned fractional derivative operators, and the radii of starlikeness and convexity. In addition, some applications of functions in the class ${\mathcal{P}}_{\tau ,\mu }(k,\delta ,\gamma )$ are also pointed out.