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

TL;DR

This paper introduces a new subclass of analytic functions defined via fractional derivatives in the complex domain, providing coefficient bounds, distortion theorems, and geometric radii for starlikeness and convexity.

Contribution

It defines a novel subclass of univalent functions using fractional derivatives and derives key geometric and coefficient inequalities for this class.

Findings

Coefficient inequalities established for the new class.

Distortion theorems involving fractional derivatives.

Radii of starlikeness and convexity determined.

Abstract

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.