Sandwich-Type Results and Existence Results of Analytic Functions Associated with the Fractional q-Calculus Operator

In the present investigation, we present certain subordination and superordination results for the q-integral operator of a fractional order associated with analytic functions in the open unit disk U. Using this q-integral operator, we obtain sandwich-type results. Furthermore, we employ the existence of univalent solutions to a q-differential equation connected with a fractional q-integral operator of fractional order. We use these results to demonstrate the significance of our findings for particular functions. We also derive some examples and corollaries that are pertinent to our results.