Trailokya Panigrahi - Institute of Mathematics and Applications, Andharua, Bhubaneswar-۷۵۱۰۲۹, Odisha, India.
Gangadharan Murugusundaramoorthy - School of Advanced Sciences, Vellore Institute of Technology, Vellore-۶۳۲۰۱۴, Tamilnadu, India.
Eureka Pattnayak - Institute of Mathematics and Applications, Andharua, Bhubaneswar-۷۵۱۰۲۹, Odisha, India.

In this paper, by employing  sine hyperbolic inverse functions,  we  introduced the generalized  subfamily \mathcal{RK}_{\sinh}(\beta) of analytic functions defined on the open unit disk \Delta:=\{\xi: \xi \in \mathbb{C} \text{ and } |\xi|<۱ \} associated with the petal-shaped domain. The bounds of the first three Taylor-Maclaurin's coefficients, Fekete-Szeg\"{o} functional and the second Hankel determinants are investigated for f\in\mathcal{RK}_{\sinh}(\beta). We considered Borel distribution as an application to our main results. Consequently, a number of corollaries have been made based on our results, generalizing previous studies in this direction.

Analytic function, Bounded turning function, convex function, Subordination, Fekete-Szego functional, Hankel determinant, Borel distribution