Analysis of coefficient functionals for analytic functions with bounded turning linked with $q$-Sine function

This research study was focused on investigating a newly defined subclass of analytic functions, denoted as $R_{{\sin }_q}$ that was affiliated with the $q$-analogue of sine function that was defined in the open unit disk. The study examined the $q$-analogue of the sine function, with a focus on analyzing the upper bound of second and third order Hankel determinants, addressing coefficient problems, investigating the Krushkal inequality and estimating certain sharp bounds for coefficient problems for the corresponding subclass $R_{{\sin }_q}$. All computed bounds were sharp.