Some Results for Third-Order Differential Subordination and Superordination Involving the Fractional Derivative and Differential Operator

In the present paper, we define a certain suitable classes of admissible functions in the open unit disk associated with fractional derivative and differential operator. We derive some third-order subordination and superordination results for these classes. These results are applied to obtain third-order differential sandwich results. In addition, we indicate certain special cases and consequences for our results.