Geometric Properties and Hardy Spaces of Rabotnov Fractional Exponential Functions

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 gamma. 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.