Geometric Properties and Hardy Spaces of Rabotnov Fractional Exponential Functions

Abstract

The aim of this study is to investigate a certain sufficiency criterion for uniform convexity, strong starlikeness, and strong convexity of Rabtonov fractional exponential functions. We also study the starlikeness and convexity of order γ. Moreover, we find conditions so that the Rabotnov functions belong to the class of bounded analytic functions and Hardy spaces. Various consequences of these results are also presented.

Keywords

• Rabotnov function
• strong convexity
• strong starlikeness
• uniformly convex functions
• starlike functions
• convex functions