Some Results on Third-Order Differential Subordination and Differential Superordination for Analytic Functions Using a Fractional Differential Operator

Abstract

In this study, we explore the implications of a third-order differential subordination in the context of analytic functions associated with fractional differential operators. Our investigation involves the consideration of specific admissible classes of third-order differential functions. We also extend this exploration to establish a dual principle, resulting in a sandwich-type outcome. We introduce these admissible function classes by employing the fractional derivative operator DzαSN,Sϑz  and derive conditions on the normalized analytic function f that lead to sandwich-type subordination in combination with an appropriate fractional differential operator.