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A novel subclass of analytic functions specified by a family of fractional derivatives in the complex domain

Esa Zainab (University Putra Malaysia, Department of Mathematics, UPM Serdang, Selangor, Malaysia)
Srivastava H.M. (University of Victoria, Department of Mathematics and Statistics, Victoria, British Columbia VW R, Canada + China Medical University, Taichung, Taiwan, Republic of China)
Kılıçman Adem (University Putra Malaysia, Department of Mathematics, UPM Serdang, Selangor, Malaysia)
Ibrahim Rabha W. (University of Malaya, Institute of Mathematical Sciences, Kuala Lumpur, Malaysia)

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 Pτ,μ(k,δ,γ) of analytic and univalent functions in the open unit disk U. In particular, for functions in the class Pτ,μ(k,δ,γ), we derive sufficient coefficient inequalities and coefficient estimates, 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 Pτ,μ(k,δ,γ) are also pointed out.

Keywords: analytic functions, univalent functions, Fractional integral and fractional derivative operators, Srivastava-Owa operator of fractional derivative, coeffecient inequalities and coefficient estimates, Distortion theorems, radii of convexity and starlikeness, modified convolution