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arXiv · 1511.01581

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

Zainab Esa·H. M. Srivastava·Adem Kilicman·Rabha W. Ibrahim
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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.

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Zainab Esa, H. M. Srivastava, Adem Kilicman, Rabha W. Ibrahim. 2015-11-05. A Novel Subclass of Analytic Functions Specified by a Family of Fractional Derivatives in the Complex Domain. https://arxiv.org/abs/1511.01581

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